%!PS-Adobe-2.0 %%Copyright: Copyright (c) 1993 AT&T, All Rights Reserved %%Version: 3.4 %%DocumentFonts: (atend) %%Pages: (atend) %%BoundingBox: (atend) %%EndComments /DpostDict 200 dict def DpostDict begin % % Copyright (c) 1993 AT&T, All Rights Reserved % % Version 3.4 prologue for troff files. % /#copies 1 store /Prologue (dpost.ps) def /aspectratio 1 def /formsperpage 1 def /landscape false def /linewidth .3 def /magnification 1 def /margin 0 def /orientation 0 def /resolution 720 def /rotation 1 def /xoffset 0 def /yoffset 0 def /roundpage true def /useclippath true def /pagebbox [0 0 612 792] def /R /Times-Roman def /I /Times-Italic def /B /Times-Bold def /BI /Times-BoldItalic def /H /Helvetica def /HI /Helvetica-Oblique def /HB /Helvetica-Bold def /HX /Helvetica-BoldOblique def /CW /Courier def /CO /Courier def /CI /Courier-Oblique def /CB /Courier-Bold def /CX /Courier-BoldOblique def /PA /Palatino-Roman def /PI /Palatino-Italic def /PB /Palatino-Bold def /PX /Palatino-BoldItalic def /Hr /Helvetica-Narrow def /Hi /Helvetica-Narrow-Oblique def /Hb /Helvetica-Narrow-Bold def /Hx /Helvetica-Narrow-BoldOblique def /KR /Bookman-Light def /KI /Bookman-LightItalic def /KB /Bookman-Demi def /KX /Bookman-DemiItalic def /AR /AvantGarde-Book def /AI /AvantGarde-BookOblique def /AB /AvantGarde-Demi def /AX /AvantGarde-DemiOblique def /NR /NewCenturySchlbk-Roman def /NI /NewCenturySchlbk-Italic def /NB /NewCenturySchlbk-Bold def /NX /NewCenturySchlbk-BoldItalic def /ZD /ZapfDingbats def /ZI /ZapfChancery-MediumItalic def /S /S def /S1 /S1 def /GR /Symbol def /inch {72 mul} bind def /min {2 copy gt {exch} if pop} bind def /setup { counttomark 2 idiv {def} repeat pop landscape {/orientation 90 orientation add def} if /scaling 72 resolution div def linewidth setlinewidth 1 setlinecap pagedimensions xcenter ycenter translate orientation rotation mul rotate width 2 div neg height 2 div translate xoffset inch yoffset inch neg translate margin 2 div dup neg translate magnification dup aspectratio mul scale scaling scaling scale addmetrics 0 0 moveto } def /pagedimensions { useclippath userdict /gotpagebbox known not and { /pagebbox [clippath pathbbox newpath] def roundpage currentdict /roundpagebbox known and {roundpagebbox} if } if pagebbox aload pop 4 -1 roll exch 4 1 roll 4 copy landscape {4 2 roll} if sub /width exch def sub /height exch def add 2 div /xcenter exch def add 2 div /ycenter exch def userdict /gotpagebbox true put } def /landscapepage { landscape not { 0 height scaling div neg translate % not quite 90 rotate } if } bind def /portraitpage { landscape { width scaling div 0 translate % not quite -90 rotate } if } bind def /addmetrics { /Symbol /S null Sdefs cf /Times-Roman /S1 StandardEncoding dup length array copy S1defs cf } def /pagesetup { /page exch def currentdict /pagedict known currentdict page known and { page load pagedict exch get cvx exec } if } def /decodingdefs [ {counttomark 2 idiv {y moveto show} repeat} {neg /y exch def counttomark 2 idiv {y moveto show} repeat} {neg moveto {2 index stringwidth pop sub exch div 0 32 4 -1 roll widthshow} repeat} {neg moveto {spacewidth sub 0.0 32 4 -1 roll widthshow} repeat} {counttomark 2 idiv {y moveto show} repeat} {neg setfunnytext} ] def /setdecoding {/t decodingdefs 3 -1 roll get bind def} bind def /w {neg moveto show} bind def /m {neg dup /y exch def moveto} bind def /done {/lastpage where {pop lastpage} if} def /f { dup /font exch def findfont exch dup /ptsize exch def scaling div dup /size exch def scalefont setfont linewidth ptsize mul scaling 10 mul div setlinewidth /spacewidth ( ) stringwidth pop def } bind def /changefont { /fontheight exch def /fontslant exch def currentfont [ 1 0 fontheight ptsize div fontslant sin mul fontslant cos div fontheight ptsize div 0 0 ] makefont setfont } bind def /sf {f} bind def /cf { dup length 2 idiv /entries exch def /chtab exch def /newencoding exch def /newfont exch def findfont dup length 1 add dict /newdict exch def {1 index /FID ne {newdict 3 1 roll put}{pop pop} ifelse} forall newencoding type /arraytype eq {newdict /Encoding newencoding put} if newdict /Metrics entries dict put newdict /Metrics get begin chtab aload pop 1 1 entries {pop def} for newfont newdict definefont pop end } bind def % % A few arrays used to adjust reference points and character widths in some % of the printer resident fonts. If square roots are too high try changing % the lines describing /radical and /radicalex to, % % /radical [0 -75 550 0] % /radicalex [-50 -75 500 0] % % Move braceleftbt a bit - default PostScript character is off a bit. % /Sdefs [ /bracketlefttp [201 500] /bracketleftbt [201 500] /bracketrighttp [-81 380] /bracketrightbt [-83 380] /braceleftbt [203 490] /bracketrightex [220 -125 500 0] /radical [0 0 550 0] /radicalex [-50 0 500 0] /parenleftex [-20 -170 0 0] /integral [100 -50 500 0] /infinity [10 -75 730 0] ] def /S1defs [ /underscore [0 80 500 0] /endash [7 90 650 0] ] def end %%EndProlog %%BeginSetup DpostDict begin mark /rotation 1 def /gotpagebbox true def /linewidth 0.5 def /xoffset 0 def /yoffset 0 def /#copies 1 store /magnification 1 def %%FormsPerPage: 1 /formsperpage 1 def %%Patch from lp %%EndPatch from lp /landscape false def /resolution 720 def setup 2 setdecoding end %%EndSetup %%Page: 0 1 %%PageBoundingBox: (atend) DpostDict begin /saveobj save def mark 1 pagesetup 10 R f (AT&T Bell Laboratories)2 993 1 2203 1740 t (Murray Hill, NJ 07974)3 916 1 2242 1860 t (Computing Science Technical Report No. 153)5 1848 1 1776 3033 t 12 B f (Usage Summary for Selected Optimization Routines)5 2673 1 1363 3327 t 10 I f (David M. Gay)2 568 1 2416 3591 t 10 R f (October 1990)1 546 1 2427 6051 t cleartomark showpage saveobj restore end %%PageBoundingBox: 125 171 414 638 %%EndPage: 0 1 %%Page: 1 2 %%PageBoundingBox: (atend) DpostDict begin /saveobj save def mark 2 pagesetup 12 B f (USAGE SUMMARY FOR SELECTED OPTIMIZATION)4 2989 1 1385 1220 t (ROUTINES)2537 1360 w (\262)3163 1300 w 10 I f (David M. Gay)2 568 1 2596 1620 t 10 BI f (CONTENTS)720 2280 w 10 R f (1. Introduction)1 669 1 795 2556 t (1a. Notation)1 550 1 1120 2676 t (1b. Caveat)1 477 1 1120 2796 t ( and reverse communication)3 1128(1c. Forward)1 538 2 1120 2916 t ( defaults)1 341(2. Overriding)1 613 2 795 3036 t ( codes)1 252(3. Return)1 447 2 795 3156 t (4. Scaling)1 475 1 795 3276 t ( scaling for regression)3 884(4a. Adaptive)1 566 2 1120 3396 t ( scaling for regression)3 884(4b. Fixed)1 428 2 1120 3516 t ( scaling for general optimization)4 1298(4c. Adaptive)1 566 2 1120 3636 t ( and V components that control scaling)6 1565(4d. IV)1 305 2 1120 3756 t ( tolerances)1 429(5. Stopping)1 537 2 795 3876 t ( output)1 281(6. Printed)1 464 2 795 3996 t ( controls)1 347(6a. Print)1 395 2 1120 4116 t ( summary)1 397(6b. Iteration)1 538 2 1120 4236 t ( routine calling sequences)3 1034(6c. Print)1 395 2 1120 4356 t ( step bound)2 461(7. Initial)1 414 2 795 4476 t ( differences)1 467(8. Finite)1 409 2 795 4596 t ( functions)1 397(9. Noisy)1 414 2 795 4716 t ( regression diagnostics, and confidence intervals)5 1935(10. Covariance,)1 704 2 745 4836 t ( \(or rejecting\))2 548(11. Identifying)1 669 2 745 4956 t 10 I f (x)1987 4956 w 10 R f (12. STOPX)1 542 1 745 5076 t (13. Restarting)1 636 1 745 5196 t ( and the PORT stack)4 827(14. INFO)1 458 2 745 5316 t ( IV components)2 638(14. Output)1 503 2 745 5436 t ( V components)2 605(15. Output)1 503 2 745 5556 t ( V components)2 605(16. Other)1 452 2 745 5676 t (17. Initial)1 464 1 745 5796 t 10 I f (S)1234 5796 w 10 R f (matrix)1309 5796 w ( values for symbolic subscripts)4 1238(18. Numerical)1 646 2 745 5916 t ( variations)1 419(19. Fortran)1 519 2 745 6036 t (References)970 6156 w 8 S1 f (__________________)720 6880 w 8 R f (\262 This is a reprint, with minor corrections noted in footnotes, of the)12 2251 1 720 6980 t 8 I f ( SELECTED OPTIMIZA-)2 839(USAGE SUMMARY FOR)2 841 2 3000 6980 t (TION ROUTINES)1 582 1 720 7080 t 8 R f (that appears in the Optimization chapter of the)7 1476 1 1322 7080 t 8 I f (PORT Mathematical Subroutine Library)3 1297 1 2818 7080 t 8 R f (manual of 1984.)2 520 1 4135 7080 t 10 R f ( Optimization)1 2077( 1 -)2 133( -)1 1414(October 16, 1990)2 696 4 720 7680 t cleartomark showpage saveobj restore end %%PageBoundingBox: 61 8 514 692 %%EndPage: 1 2 %%Page: 2 3 %%PageBoundingBox: (atend) DpostDict begin /saveobj save def mark 3 pagesetup 10 R f (Optimization Usage Summary)2 1216 1 720 480 t 8 R f (PORT)4548 480 w 10 R f (library)4774 480 w 10 B f (1. Introduction)1 670 1 720 840 t 10 R f ( interface, all similar to that)5 1149(Several PORT optimization routines have a common structure and user)9 2921 2 970 996 t ( are con-)2 360( controls and tolerances \320 and all scratch storage \320 used by these routines)13 3110( All)1 185(described in [2].)2 665 4 720 1116 t ( V for floating-point values \(REAL in the single-precision ver-)9 2564( for integer values,)3 763( IV)1 160(tained in two arrays:)3 833 4 720 1236 t ( not address the)3 645(sions, DOUBLE PRECISION in the double-precision versions\); this usage summary does)10 3675 2 720 1356 t ( \(e.g. SN2F and SMNF\) that allocate these arrays for you from the)12 2819(simplified versions of these routines)4 1501 2 720 1476 t ( subscripts, such as IV\(MXITER\), in describing various)7 2268( discussions below use symbolic)4 1324( The)1 211(PORT stack.)1 517 4 720 1596 t ( also given)2 441( values for these symbolic subscripts appear in \24718 and are)10 2381( Numerical)1 474(components of IV and V.)4 1024 4 720 1716 t ( discussed, as in ``IV\(MXITER\) = IV\(18\) is the maximum number of iterations)12 3411(when a component is)3 909 2 720 1836 t ( this is)2 268( exception is the first component of IV, IV\(1\), which on input says what kind of call)16 3394(allowed.'' \(One)1 658 3 720 1956 t ( is always called IV\(1\).\))4 961( It)1 111(and on output contains a return code.)6 1478 3 720 2076 t ( to encompass some routines that will not be included in the initial)12 2799(This usage summary is written)4 1271 2 970 2232 t (release of PORT 3, such as routines for nonlinear Poisson, logistic, and robust regression and versions of)16 4320 1 720 2352 t ( summary is designed to)4 1060( This)1 250( handle general linear constraints.)4 1432(the various optimization routines that)4 1578 4 720 2472 t (remain valid when such routines are added to the library.)9 2273 1 720 2592 t 10 B f (1a. Notation)1 547 1 720 2832 t 10 R f (Given a function)2 687 1 970 2988 t 10 I f (f)1690 2988 w 10 R f (of)1751 2988 w 10 I f (p)1867 2988 w 10 R f ( attempt to find a)4 719(variables, the optimization routines)3 1434 2 1950 2988 t 10 I f (p)4137 2988 w 10 R f (-vector)4187 2988 w 10 I f (x *)1 102 1 4503 2988 t 10 R f (that mini-)1 401 1 4639 2988 t (mizes)720 3108 w 10 I f (f)978 3108 w 10 R f (\()1022 3108 w 10 I f (x)1063 3108 w 10 R f ( constraints may be imposed on)5 1263(\). Various)1 424 2 1115 3108 t 10 I f (x)2827 3108 w 10 R f (: none, simple bounds of the form)6 1352 1 2871 3108 t 10 I f (b)2621 3293 w 10 S f (_)2619 3293 w 7 I f (x)2682 3253 w 10 S f (\243)2762 3293 w 10 I f (x)2858 3293 w 10 S f (\243)2943 3293 w 10 I f (b)3039 3293 w 10 S1 f (_)3044 3200 w 7 I f (x)3100 3224 w 10 R f (\(1.1\))4849 3293 w (\(where)720 3478 w 10 I f (b)1031 3478 w 10 S f (_)1029 3478 w 7 I f (x)1092 3438 w 10 R f (and)1166 3478 w 10 I f (b)1345 3478 w 10 S1 f (_)1350 3385 w 7 I f (x)1406 3409 w 10 R f ( the inequalities are understood componentwise\), or general linear con-)9 2937(are vectors and)2 623 2 1480 3478 t (straints of the form)3 763 1 720 3598 t 10 I f (b)2587 3783 w 10 S f (_)2585 3783 w 7 I f (c)2648 3743 w 10 S f (\243)2728 3783 w 10 I f (Cx)2824 3783 w 10 S f (\243)2976 3783 w 10 I f (b)3072 3783 w 10 S1 f (_)3077 3690 w 7 I f (c)3133 3714 w 10 R f (\(1.2\))4849 3783 w (\(where)720 3968 w 10 I f (b)1023 3968 w 10 S f (_)1021 3968 w 7 I f (c)1084 3928 w 10 R f (and)1150 3968 w 10 I f (b)1322 3968 w 10 S1 f (_)1327 3875 w 7 I f (c)1383 3899 w 10 R f (are vectors and)2 609 1 1450 3968 t 10 I f (C)2087 3968 w 10 R f ( gradient of)2 466( The)1 208(is a matrix\).)2 486 3 2182 3968 t 10 I f (f)3370 3968 w 10 R f (at)3426 3968 w 10 I f (x)3526 3968 w 10 R f (\(vector of first partial derivatives of)5 1442 1 3598 3968 t 10 I f (f)720 4088 w 10 R f (\) will be denoted by)4 847 1 748 4088 t 10 S f (\321)1632 4088 w 10 I f (f)1719 4088 w 10 R f (\()1763 4088 w 10 I f (x)1804 4088 w 10 R f (\), and the Hessian of)4 867 1 1856 4088 t 10 I f (f)2759 4088 w 10 R f (at)2823 4088 w 10 I f (x)2931 4088 w 10 R f (\(matrix of second partial derivatives of)5 1610 1 3011 4088 t 10 I f (f)4657 4088 w 10 R f (\) will be)2 355 1 4685 4088 t (denoted by)1 441 1 720 4208 t 10 S f (\321)1186 4208 w 7 R f (2)1262 4168 w 10 I f (f)1321 4208 w 10 R f (\()1365 4208 w 10 I f (x)1406 4208 w 10 R f (\).)1458 4208 w (If)970 4364 w 10 I f (z)1078 4364 w 10 R f (is a vector of)3 569 1 1159 4364 t 10 I f (m)1770 4364 w 10 R f (components,)1884 4364 w 10 I f (z)2434 4364 w 10 S f (=)2522 4364 w 10 R f (\()2626 4364 w 10 I f (z)2667 4364 w 7 R f (1)2717 4384 w 10 R f (,)2768 4364 w 10 I f (z)2825 4364 w 7 R f (2)2875 4384 w 10 R f (,)2926 4364 w (. . .)2 125 1 3008 4339 t (,)3166 4364 w 10 I f (z)3223 4364 w 7 I f (m)3273 4384 w 10 R f (\))3339 4364 w 7 I f (T)3383 4324 w 10 R f (, then)1 239 1 3430 4364 t 10 S f (\357 \357)1 73 1 3711 4381 t 10 I f (z)3783 4364 w 10 S f (\357 \357)1 73 1 3822 4381 t 10 R f (denotes its Euclidean norm)3 1136 1 3904 4364 t (\(2\261norm\),)720 4484 w 10 S f (\357 \357)1 73 1 2442 4766 t 10 I f (z)2514 4749 w 10 S f (\357 \357)1 73 1 2553 4766 t (=)2666 4749 w (\351)2778 4662 w (\357)2778 4762 w (\353)2778 4862 w 7 I f (i)2828 4849 w 7 S f (=)2864 4849 w 7 R f (1)2914 4849 w 15 S f (S)2844 4779 w 7 I f (m)2864 4649 w 10 I f (z)2990 4749 w 7 I f (i)3034 4768 w 7 R f (2)3034 4709 w 10 S f (\371)3077 4662 w (\357)3077 4762 w (\373)3077 4862 w 7 R f (1)3143 4610 w 8 I f (/)3199 4610 w 7 R f (2)3242 4610 w 10 I f (.)3293 4749 w 10 R f (\(1.3\))4849 4749 w 9 B f (MACHEP)970 5070 w 10 R f ( V values, denotes the unit roundoff on the)8 1746(, which appears in some expressions for default)7 1924 2 1370 5070 t (current machine \(the value returned by the PORT function)8 2334 1 720 5190 t 10 CW f (R1MACH\(4\))3079 5190 w 10 R f (or)3644 5190 w 10 CW f (D1MACH\(4\))3752 5190 w 10 R f (\).)4292 5190 w 10 B f (1b. Caveat)1 480 1 720 5430 t 10 R f (Unless)970 5586 w 10 I f (f)1283 5586 w 10 R f ( when)1 258(is convex, the PORT optimization routines may only find a local minimum, even)12 3430 2 1352 5586 t ( you think this is a danger, you may wish to try several starting points.)14 2810( When)1 288(``better'' minima exist.)2 929 3 720 5706 t 10 B f ( and reverse communication)3 1207(1c. Forward)1 546 2 720 5946 t 10 R f (The optimization routines addressed by this usage summary have at least two levels:)12 3374 1 970 6102 t 10 S f (\267)1120 6282 w 10 R f (forward-communication routine)1 1278 1 1191 6282 t 10 S f (\267)1120 6402 w 10 R f (reverse-communication iteration driver)2 1563 1 1191 6402 t (Forward-communication routines learn about)3 1847 1 720 6582 t 10 I f (f)2605 6582 w 10 R f (\()2649 6582 w 10 I f (x)2690 6582 w 10 R f ( give them a subroutine)4 990( you)1 213(\) in the conventional way:)4 1095 3 2742 6582 t ( compute)1 369(they can call to)3 610 2 720 6702 t 10 I f (f)1724 6702 w 10 R f (\()1768 6702 w 10 I f (x)1809 6702 w 10 R f ( drivers, on the other hand, return to their caller \(e.g.)10 2095(\). Reverse-communication)1 1084 2 1861 6702 t ( know)1 253(your main program\) whenever they need to)6 1759 2 720 6822 t 10 I f (f)2763 6822 w 10 R f (\()2807 6822 w 10 I f (x)2848 6822 w 10 R f (\) at a new)3 408 1 2900 6822 t 10 I f (x)3339 6822 w 10 R f ( calling routine must then compute)5 1421(. The)1 236 2 3383 6822 t (the necessary information \(e.g.)3 1263 1 720 6942 t 10 I f (f)2018 6942 w 10 R f (\()2062 6942 w 10 I f (x)2103 6942 w 10 R f (\) itself or, for some regression routines, a residual vector\) and call the)12 2885 1 2155 6942 t ( it is easier to use a)6 886( Usually)1 382( again, passing it the information it wants.)7 1827(reverse-communication driver)1 1225 4 720 7062 t ( call a reverse-communication)3 1223(forward-communication optimization routine, but sometimes it is simpler to)8 3097 2 720 7182 t (driver, e.g. when writing a subroutine that computes)7 2086 1 720 7302 t 10 I f (f)2831 7302 w 10 R f (\()2875 7302 w 10 I f (x)2916 7302 w 10 R f (\) is inconvenient.)2 691 1 2968 7302 t ( 16, 1990)2 375( October)1 1702( 2 -)2 133(Optimization -)1 2110 4 720 7680 t cleartomark showpage saveobj restore end %%PageBoundingBox: 61 8 514 764 %%EndPage: 2 3 %%Page: 3 4 %%PageBoundingBox: (atend) DpostDict begin /saveobj save def mark 4 pagesetup 8 R f (PORT)720 480 w 10 R f ( Usage Summary)2 688(library Optimization)1 3406 2 946 480 t ( versions of the optimization routines receive IV)7 2017(Both the forward- and the reverse-communication)5 2053 2 970 840 t ( to the reverse-communication drivers also include)6 2048( Parameters)1 497(and V as parameters.)3 848 3 720 960 t 10 I f (x)4142 960 w 10 R f ( as either the)3 516(, as well)2 338 2 4186 960 t (values of)1 375 1 720 1080 t 10 I f (f)1132 1080 w 10 R f (\()1176 1080 w 10 I f (x)1217 1080 w 10 R f (\) and perhaps)2 561 1 1269 1080 t 10 S f (\321)1867 1080 w 10 I f (f)1954 1080 w 10 R f (\()1998 1080 w 10 I f (x)2039 1080 w 10 R f ( to compute these values \(for regression rou-)7 1873(\) or information sufficient)3 1076 2 2091 1080 t ( driver returns with IV\(1\) = 1 when it wants to have)11 2077(tines\). The)1 454 2 720 1200 t 10 I f (f)3277 1200 w 10 R f (evaluated at the current)3 936 1 3331 1200 t 10 I f (x)4293 1200 w 10 R f (and with IV\(1\) =)3 677 1 4363 1200 t (2 when it wants)3 642 1 720 1320 t 10 S f (\321)1391 1320 w 10 I f (f)1478 1320 w 10 R f ( IV\(1\) = \2611 or \2612; see the)7 1047( drivers have other possible returns, such as)7 1769(evaluated. Some)1 689 3 1535 1320 t (appropriate PORT reference sheet for details.)5 1811 1 720 1440 t 10 B f ( defaults)1 364(2. Overriding)1 603 2 720 1680 t 10 R f ( may run)2 365( You)1 227( two arrays, IV and V.)5 914(As explained above, input controls and tolerances are passed in)9 2564 4 970 1836 t ( input components at their default values by setting IV\(1\) to 0 before calling the optimiza-)15 3613(with all IV and V)4 707 2 720 1956 t ( you may need to relax)5 952( Sometimes)1 503( sections below.\))2 690( values are described in various)5 1290( \(Default)1 389(tion routine.)1 496 6 720 2076 t ( To)1 163(the default stopping tolerances, turn off some of the default printing, or otherwise turn the input knobs.)16 4157 2 720 2196 t ( double\) to supply IV and V with)7 1366(do so, you first call subroutine IVSET \(for single precision, DIVSET for)11 2954 2 720 2316 t ( you)1 185( Finally,)1 369( of IV and V.)4 569( then assign nondefault values to appropriate components)7 2371( You)1 233(default values.)1 593 6 720 2436 t ( calling sequence for IVSET is)5 1228( The)1 205(call the relevant optimization routine, passing IV and V to it.)10 2431 3 720 2556 t 10 CW f (CALL IVSET\(KIND, IV, LIV, LV, V\))5 1920 1 1070 2796 t 10 R f (where)720 3036 w 10 CW f (KIND)998 3036 w 10 R f ( as in Table 1 below \320 and specified on the relevant PORT reference)13 2922(is an integer, chosen)3 845 2 1273 3036 t (sheet as well.)2 535 1 720 3156 t 10 S f (_ _____________________________________________________)1 2674 1 1543 3236 t 10 CW f (KIND)1593 3356 w 10 R f (Kind of optimization)2 839 1 2655 3356 t 10 S f (_ _____________________________________________________)1 2674 1 1543 3376 t 10 R f ( or simply bounded regression)4 1210(1 unconstrained)1 855 2 1688 3496 t ( or simply bounded general optimization)5 1624(2 unconstrained)1 855 2 1688 3616 t ( with general linear constraints)4 1231(3 regression)1 705 2 1688 3736 t ( optimization with general linear constraints)5 1762(4 general)1 588 2 1688 3856 t 10 S f ( \347)1 -2674(_ _____________________________________________________)1 2674 2 1543 3876 t (\347)1543 3836 w (\347)1543 3736 w (\347)1543 3636 w (\347)1543 3536 w (\347)1543 3436 w (\347)1543 3336 w (\347)4217 3876 w (\347)4217 3836 w (\347)4217 3736 w (\347)4217 3636 w (\347)4217 3536 w (\347)4217 3436 w (\347)4217 3336 w 10 R f (Table 1)1 302 1 2729 4176 t ( PORT)1 285( The)1 209( providing.)1 443(The integer parameters LIV and LV give the lengths of the IV and V arrays you are)16 3383 4 720 4416 t ( acceptable values for LIV and LV, val-)7 1589(reference sheet for the relevant optimization routine gives minimum)8 2731 2 720 4536 t ( is usually simplest to be liberal in choosing LIV and)10 2186( It)1 118( of the problem dimensions.)4 1147(ues that are functions)3 869 4 720 4656 t ( long as you do not run out of stor-)9 1409(LV \320 to guess \(or compute\) overestimates of their minimum values; so)11 2911 2 720 4776 t ( you make LIV or LV too small)7 1324( If)1 124( necessary should cause no harm.)5 1370(age, making LIV and LV larger than)6 1502 4 720 4896 t ( stored\), then a)3 614(\(but make LIV at least 21, so that the printing unit number, IV\(PRUNIT\) = IV\(21\) can be)16 3706 2 720 5016 t ( \(if LIV is at least 45\))6 877( Also,)1 266(message giving the minimum acceptable values of LIV and LV will be printed.)12 3177 3 720 5136 t ( routine will store these minimum LIV and LV values in IV\(LASTIV\) = IV\(44\) and)14 3645(the optimization)1 675 2 720 5256 t (IV\(LASTV\) = IV\(45\) respectively.)3 1402 1 720 5376 t 10 BI f (Example:)970 5532 w 10 R f ( off all printing when calling an unconstrained general optimization routine \(e.g.,)11 3311(To turn)1 303 2 1426 5532 t (MNF or MNG\), execute)3 970 1 720 5652 t 10 CW f (CALL IVSET\(2, IV, LIV, LV, V\))5 1740 1 1070 5892 t (IV\(19\) = 0)2 600 1 1070 6012 t 10 R f (See \2476a for more information on print controls.)7 1892 1 720 6252 t 10 B f ( codes)1 258(3. Return)1 430 2 720 6492 t 10 R f ( a return code \(a number that indicates how the)9 1903(When the optimization routines return, IV\(1\) contains)6 2167 2 970 6648 t ( meanings of these return codes)5 1261( The)1 205( 6.)1 100( desirable return codes are 3, 4, 5, and sometimes)9 1977( The)1 206(routine fared\).)1 571 6 720 6768 t ( codes include:)2 599( Return)1 322(are sketched in the list of return codes below and described in more detail in \2475.)15 3194 3 720 6888 t ( Optimization)1 2077( 3 -)2 133( -)1 1414(October 16, 1990)2 696 4 720 7680 t cleartomark showpage saveobj restore end %%PageBoundingBox: 61 8 514 764 %%EndPage: 3 4 %%Page: 4 5 %%PageBoundingBox: (atend) DpostDict begin /saveobj save def mark 5 pagesetup 10 R f (Optimization Usage Summary)2 1216 1 720 480 t 8 R f (PORT)4548 480 w 10 R f (library)4774 480 w 10 I f (Favorable returns:)1 763 1 1220 840 t 10 R f ( are input IV\(1\) values only \(see \2471c\).)7 1518(1\2612 \320 impossible: these)3 1067 2 870 1140 t ( appears to be a scaled distance \(see \2475\) of at most)11 2344( current iterate)2 639( the)1 201(3 \320 X-convergence:)2 886 4 970 1320 t (V\(XCTOL\) = V\(33\) from a locally optimal point.)7 1987 1 1220 1440 t ( current objective function value)4 1313( the)1 176( function convergence:)2 920(4 \320 relative)2 549 4 970 1620 t 10 I f (f)3957 1620 w 10 R f (\()4001 1620 w 10 I f (x)4042 1620 w 10 R f (\) appears to differ from)4 946 1 4094 1620 t (a locally optimal value by at most)6 1355 1 1220 1740 t 10 S f (\357)2600 1757 w 10 I f (f)2656 1740 w 10 R f (\()2700 1740 w 10 I f (x)2741 1740 w 10 R f (\))2793 1740 w 10 S f (\357)2826 1757 w 10 R f (.)2898 1710 w ( =)1 81(V \( RFCTOL \))3 546 2 2955 1740 t 10 S f (\357)3607 1757 w 10 I f (f)3663 1740 w 10 R f (\()3707 1740 w 10 I f (x)3748 1740 w 10 R f (\))3800 1740 w 10 S f (\357)3833 1757 w 10 R f (.)3905 1710 w (V \( 32 \).)3 287 1 3962 1740 t ( X- and relative function convergence \(3 and 4 combined\).)9 2338(5 \320 both)2 428 2 970 1920 t ( function convergence:)2 920(6 \320 absolute)2 583 2 970 2100 t 10 S f (\357)2526 2117 w 10 I f (f)2582 2100 w 10 R f (\()2626 2100 w 10 I f (x)2667 2100 w 10 R f (\))2719 2100 w 10 S f (\357)2752 2117 w (<)2800 2100 w 10 R f ( is only of interest in)5 845( test)1 167( This)1 231( = V\(31\).)2 375(V \( AFCTOL \))3 551 5 2871 2100 t (problems where)1 640 1 1220 2220 t 10 I f (f)1885 2220 w 10 R f (\()1929 2220 w 10 I f (x)1970 2220 w 10 R f (\))2022 2220 w 10 S f (=)2112 2220 w 10 R f (0 means a ``perfect fit'', such as nonlinear least-squares problems.)9 2651 1 2216 2220 t 10 I f (Error returns from which restarts \(\24713\) are possible:)7 2136 1 1220 2460 t 10 R f ( convergence:)1 556(7 \320 singular)2 572 2 970 2760 t 10 I f (x)2148 2760 w 10 R f ( \2475.)1 150( See)1 194(may have too many free components.)5 1497 3 2217 2760 t ( gradient)1 357( the)1 177( convergence:)1 561(8 \320 false)2 438 4 970 2940 t 10 S f (\321)2533 2940 w 10 I f (f)2620 2940 w 10 R f (\()2664 2940 w 10 I f (x)2705 2940 w 10 R f ( incorrectly, the other stopping toler-)5 1500(\) may be computed)3 783 2 2757 2940 t (ances may be too tight, or either)6 1284 1 1220 3060 t 10 I f (f)2529 3060 w 10 R f (or)2582 3060 w 10 S f (\321)2690 3060 w 10 I f (f)2777 3060 w 10 R f (may be discontinuous near the current iterate)6 1796 1 2830 3060 t 10 I f (x)4651 3060 w 10 R f (.)4695 3060 w ( convergence after IV\(MXFCAL\) = IV\(17\) evaluations of)7 2313( no)1 150( evaluation limit:)2 684(9 \320 function)2 583 4 970 3240 t 10 I f (f)4725 3240 w 10 R f (\()4769 3240 w 10 I f (x)4810 3240 w 10 R f (\).)4862 3240 w ( convergence after IV\(MXITER\) = IV\(18\) iterations.)6 2113( no)1 150( limit:)1 243(10 \320 iteration)2 633 4 920 3420 t ( supplied a system-dependent STOPX \(see \24712\) routine and hit)9 2567( you)1 205( returned .TRUE.:)2 731(11 \320 STOPX)2 617 4 920 3600 t (the BREAK key.)2 680 1 1220 3720 t ( means allocate storage within IV and V and)8 1782( \(12)1 184( are input IV\(1\) values only.)5 1136( these)1 256(12\26113 \320 impossible:)2 912 5 770 3900 t ( means just allo-)3 676( 13)1 156( is the default IV\(1\) value supplied by [D]IVSET.)8 2036(start the algorithm; this)3 952 4 1220 4020 t ( \2474a for an example.\))4 850( See)1 194(cate storage and return.)3 930 3 1220 4140 t ( has been allocated \(after a call with IV\(1\) = 13 \320 see, for example, \2474a below\).)16 3216(14 \320 storage)2 588 2 920 4320 t 10 I f (Error returns that preclude restarts:)4 1461 1 1220 4560 t 10 R f ( too small.)2 420(15 \320 LIV)2 466 2 920 4860 t ( too small.)2 420(16 \320 LV)2 433 2 920 5040 t ( attempted \(\24713\) with problem dimensions changed.)6 2084(17 \320 restart)2 549 2 920 5220 t (18 \320)1 250 1 920 5400 t 10 I f (d)1220 5400 w 10 R f (has a negative component and IV\(DTYPE\))5 1721 1 1295 5400 t 10 S f (\243)3041 5400 w 10 R f ( \2474.)1 150(0: see)1 255 2 3121 5400 t ( is out of range.)4 624(19\26143 \320 V\(IV\(1\)\))2 809 2 770 5580 t (44\26162 \320 reserved.)2 812 1 770 5760 t (63 \320)1 250 1 920 5940 t 10 I f (f)1220 5940 w 10 R f (\()1264 5940 w 10 I f (x)1305 5940 w 10 R f (\) cannot be computed at the initial)6 1365 1 1357 5940 t 10 I f (x)2747 5940 w 10 R f (.)2791 5940 w ( parameters on an internal call \(should not occur\).)8 1987(64 \320 bad)2 444 2 920 6120 t ( gradient could not be computed at)6 1387(65 \320 the)2 422 2 920 6300 t 10 I f (x)2754 6300 w 10 R f (.)2798 6300 w ( input array \320 if this return is relevant, the associated PORT reference sheet will say so and)17 3676(66 \320 bad)2 444 2 920 6480 t (explain what is good and bad.)5 1193 1 1220 6600 t ( first parameter \()3 667(67 \320 bad)2 444 2 920 6780 t 10 CW f (KIND)2031 6780 w 10 R f (in \2472\) to IVSET.)3 672 1 2296 6780 t ( encountered \(should not occur\).)4 1294(68\26169 \320 bugs)2 639 2 770 6960 t ( get initial)2 442(70 \320 couldn't)2 633 2 920 7140 t 10 I f (S)2038 7140 w 10 R f ( only when)2 482(matrix by finite differences \(regression routines only, and)7 2427 2 2131 7140 t ( [The)1 241(IV\(INITS\) is at least 3\).)4 968 2 1220 7260 t 10 I f (S)2457 7260 w 10 R f (matrix is an approximation to part of the Hessian matrix,)9 2288 1 2534 7260 t 10 S f (\321)4849 7260 w 7 R f (2)4925 7220 w 10 I f (f)4984 7260 w 10 R f (;)5012 7260 w ( 16, 1990)2 375( October)1 1702( 4 -)2 133(Optimization -)1 2110 4 720 7680 t cleartomark showpage saveobj restore end %%PageBoundingBox: 61 8 514 764 %%EndPage: 4 5 %%Page: 5 6 %%PageBoundingBox: (atend) DpostDict begin /saveobj save def mark 6 pagesetup 8 R f (PORT)720 480 w 10 R f ( Usage Summary)2 688(library Optimization)1 3406 2 946 480 t (see [1] for details.])3 753 1 1220 840 t (71\26179 \320 reserved.)2 812 1 770 1020 t ( was out of range \(e.g. exceeded 14\).)7 1467(80 \320 IV\(1\))2 521 2 920 1200 t ( regression routines,)2 837( problem dimensions \(e.g. a nonpositive number of variables or, for)10 2839(81 \320 bad)2 444 3 920 1380 t (number of observations\).)2 1001 1 1220 1500 t ( bounds in \(1.1\):)3 661(82 \320 inconsistent)2 778 2 920 1686 t 10 I f (b)2409 1686 w 10 S f (_)2407 1686 w 7 I f (i)2464 1705 w (x)2464 1646 w 10 S f (>)2552 1686 w 10 I f (b)2656 1686 w 10 S1 f (_)2661 1593 w 7 I f (i)2711 1705 w (x)2711 1618 w 10 R f (for some)1 352 1 2775 1686 t 10 I f (i)3152 1686 w 10 R f (.)3180 1686 w ( bounds in \(1.2\):)3 661(83 \320 inconsistent)2 778 2 920 1872 t 10 I f (b)2409 1872 w 10 S f (_)2407 1872 w 7 I f (i)2464 1891 w (c)2464 1832 w 10 S f (>)2552 1872 w 10 I f (b)2656 1872 w 10 S1 f (_)2661 1779 w 7 I f (i)2711 1891 w (c)2711 1804 w 10 R f (for some)1 352 1 2775 1872 t 10 I f (i)3152 1872 w 10 R f (.)3180 1872 w ( row of the constraint matrix,)5 1165(84 \320 some)2 511 2 920 2052 t 10 I f (C)2621 2052 w 10 R f (in \(1.2\), is all zeros.)4 796 1 2713 2052 t ( is no)2 225( there)1 253( constraints:)1 490(85 \320 inconsistent)2 778 4 920 2232 t 10 I f (x)2695 2232 w 10 R f ( that handle)2 476( \(Routines)1 444(that satisfies both \(1.1\) and \(1.2\).)5 1351 3 2769 2232 t (general linear constraints let you specify both \(1.1\) and \(1.2\).\))9 2478 1 1220 2352 t 10 B f (4. Scaling)1 437 1 720 2592 t 10 R f (A scale vector)2 586 1 970 2748 t 10 I f (d)1589 2748 w 10 S f (=)1688 2748 w 10 R f (\()1792 2748 w 10 I f (d)1833 2748 w 7 R f (1)1894 2768 w 10 R f (,)1945 2748 w 10 I f (d)2002 2748 w 7 R f (2)2063 2768 w 10 R f (,)2114 2748 w (. . .)2 125 1 2196 2723 t (,)2354 2748 w 10 I f (d)2411 2748 w 7 I f (p)2472 2768 w 10 R f ( trial)1 195(\) is used both in the convergence tests and in computing)10 2322 2 2523 2748 t (values of)1 374 1 720 2868 t 10 I f (x)1130 2868 w 10 R f ( default, the)2 494( By)1 177( affect the performance of the optimization codes.)7 2059( choice can profoundly)3 950(. Its)1 186 5 1174 2868 t ( choose)1 306(regression routines)1 760 2 720 2988 t 10 I f (d)1815 2988 w 10 R f (adaptively \(since a reasonable choice is available in this case from the associ-)12 3146 1 1894 2988 t (ated Jacobian matrix\), but the general optimization routines require you to provide)11 3328 1 720 3108 t 10 I f (d)4076 3108 w 10 R f (as an input parameter.)3 887 1 4153 3108 t ( regression routines allocate storage for)5 1581(\(The higher level)2 689 2 720 3228 t 10 I f (d)3017 3228 w 10 R f (within V \320 see \2474b and \2474d.\))6 1219 1 3094 3228 t 10 I f (d)4365 3228 w 10 R f (should be such)2 598 1 4442 3228 t (that)720 3348 w 10 S f (\357)897 3365 w 10 I f (d)945 3348 w 7 I f (i)1006 3368 w 10 R f (.)1042 3318 w 10 I f (x)1075 3348 w 7 I f (i)1130 3368 w 10 S f (\357)1158 3365 w 10 R f ( in comparable units\), 1)4 950(are all ``comparable'' \(e.g. are)4 1224 2 1201 3348 t 10 S f (\243)3416 3348 w 10 I f (i)3512 3348 w 10 S f (\243)3581 3348 w 10 I f (p)3677 3348 w 10 R f ( you can get a reasonable)5 1010(. Often)1 303 2 3727 3348 t (choice of)1 368 1 720 3478 t 10 I f (d)1113 3478 w 10 R f (by guessing upper bounds)3 1041 1 1188 3478 t 10 S f (x)2254 3478 w 7 I f (i)2314 3498 w 10 R f (on)2367 3478 w 10 S f (\357)2492 3495 w 10 I f (x)2540 3478 w 7 I f (i)2595 3498 w 10 I f (*)2611 3478 w 10 S f (\357)2661 3495 w 10 R f (and setting)1 436 1 2702 3478 t 10 I f (d)3163 3478 w 7 I f (i)3224 3498 w 10 R f (:)3293 3478 w 10 S f (=)3337 3478 w 10 R f (1)3441 3478 w 13 I f (/)3523 3478 w 10 S f (x)3567 3478 w 7 I f (i)3627 3498 w 10 R f (.)3655 3478 w ( naturally well scaled in the sense that)7 1524(Many problems are)2 776 2 970 3634 t 10 I f (d)3296 3634 w 7 I f (i)3357 3654 w 10 R f (:)3426 3634 w 10 S f (=)3470 3634 w 10 R f (1 for all)2 318 1 3574 3634 t 10 I f (i)3918 3634 w 10 R f ( can have)2 378( You)1 223(works well.)1 467 3 3972 3634 t 10 I f (d)720 3754 w 10 R f ( general optimiza-)2 728( \(For)1 223( to 0.)2 205(set to all ones by setting V\(DINIT\) = V\(38\) to 1.0 and IV\(DTYPE\) = IV\(16\))14 3087 4 797 3754 t (tion, IV\(DTYPE\) is 0 by default, so it is unnecessary to change it in this case.\))15 3135 1 720 3874 t (Below it will be convenient to let)6 1399 1 970 4030 t 10 I f (D)2405 4030 w 10 R f ( diagonal matrix whose)3 971(denote the)1 424 2 2513 4030 t 10 I f (i)3945 4030 w 10 R f (th diagonal element is)3 916 1 3973 4030 t 10 I f (d)4926 4030 w 7 I f (i)4987 4050 w 10 R f (,)5015 4030 w (where)720 4150 w 10 I f (d)988 4150 w 10 R f (is the current scale vector:)4 1047 1 1063 4150 t 10 I f (D)2261 4330 w 10 S f (=)2382 4330 w 10 R f (diag \()1 213 1 2486 4330 t 10 I f (d)2707 4330 w 7 R f (1)2768 4350 w 10 R f (,)2819 4330 w 10 I f (d)2885 4330 w 7 R f (2)2946 4350 w 10 R f (,)2997 4330 w (. . .)2 125 1 3088 4305 t (,)3246 4330 w 10 I f (d)3312 4330 w 7 I f (p)3373 4350 w 10 R f (\))3424 4330 w 10 I f (.)3473 4330 w 10 R f (\(4.1\))4849 4330 w ( various IV and V components connected with scaling; \2474d summarizes the)11 3136(\247\2474a\261c below describe)2 934 2 970 4546 t (relevant symbolic subscripts and default input values.)6 2145 1 720 4666 t 10 B f ( scaling for regression)3 935(4a. Adaptive)1 564 2 720 4906 t 10 R f (Associated with regression problems is an)5 1719 1 970 5062 t 10 I f (n)2722 5062 w 10 S f (\264)2780 5062 w 10 I f (p)2843 5062 w 10 R f (Jacobian matrix)1 643 1 2926 5062 t 10 I f (J)3602 5062 w 10 R f (\(described further on the relevant)4 1361 1 3679 5062 t ( Let)1 198(PORT reference sheet\).)2 968 2 720 5182 t 10 I f (J)1926 5182 w 7 I f (i)1981 5202 w 10 R f (denote the)1 428 1 2049 5182 t 10 I f (i)2517 5182 w 10 R f (th column of)2 541 1 2545 5182 t 10 I f (J)3126 5182 w 10 R f (,)3170 5182 w 10 I f (J)3235 5182 w 7 I f (i)3290 5202 w 10 S f (=)3367 5182 w 10 R f (\()3471 5182 w 10 I f (J)3512 5182 w 7 R f (1 ,)1 58 1 3567 5202 t 7 I f (i)3630 5202 w 10 R f (,)3666 5182 w 10 I f (J)3723 5182 w 7 R f (2 ,)1 58 1 3778 5202 t 7 I f (i)3841 5202 w 10 R f (,)3877 5182 w (. . .)2 125 1 3959 5157 t (,)4117 5182 w 10 I f (J)4174 5182 w 7 I f (n)4229 5202 w 7 R f (,)4269 5202 w 7 I f (i)4292 5202 w 10 R f (\))4328 5182 w 7 I f (T)4372 5142 w 10 R f ( adaptive)1 377(. The)1 244 2 4419 5182 t (choice of)1 368 1 720 5302 t 10 I f (d)1113 5302 w 7 I f (i)1174 5322 w 10 R f (uses the norm \(1.3\) of)4 879 1 1227 5302 t 10 I f (J)2131 5302 w 7 I f (i)2186 5322 w 10 R f (to update)1 369 1 2239 5302 t 10 I f (d)2633 5302 w 7 I f (i)2694 5322 w 10 R f (every time a new)3 684 1 2747 5302 t 10 I f (J)3456 5302 w 10 R f (is computed:)1 514 1 3525 5302 t 10 I f (d)2151 5482 w 7 I f (i)2212 5502 w 10 R f (:)2281 5482 w 10 S f (=)2325 5482 w 10 R f (max { V \( DFAC \))5 665 1 2429 5482 t (.)3110 5452 w 10 I f (d)3143 5482 w 7 I f (i)3204 5502 w 10 R f (,)3240 5482 w 10 S f (\357 \357)1 73 1 3298 5499 t 10 I f (J)3370 5482 w 7 I f (i)3425 5502 w 10 S f (\357 \357)1 73 1 3453 5499 t 10 R f ( \(4.2\))1 1431(} ;)1 84 2 3525 5482 t (if)2250 5662 w 10 I f (d)2352 5662 w 7 I f (i)2413 5682 w 10 S f (<)2490 5662 w 10 I f (DTOL)2594 5662 w 7 I f (i)2861 5682 w 10 R f (then)2930 5662 w 10 I f (d)3143 5662 w 7 I f (i)3204 5682 w 10 R f (:)3273 5662 w 10 S f (=)3317 5662 w 10 I f (d)3421 5662 w 10 S f (\260)3471 5662 w 7 I f (i)3482 5682 w 10 R f (\(4.3\))4849 5662 w (for 1)1 194 1 720 5842 t 10 S f (\243)955 5842 w 10 I f (i)1051 5842 w 10 S f (\243)1120 5842 w 10 I f (p)1216 5842 w 10 R f (. The)1 234 1 1266 5842 t 10 I f (DTOL)1529 5842 w 10 R f (and)1814 5842 w 10 I f (d)1987 5842 w 10 S f (\260)2045 5842 w 10 R f (arrays are stored in V and initialized as explained in \2474d below; the fac-)13 2926 1 2114 5842 t ( to keep)2 316( factor is included)3 721( This)1 229(tor V\(DFAC\) = V\(41\) that appears in \(4.2\) is 0.6 by default.)11 2413 4 720 5962 t 10 I f (d)4424 5962 w 7 I f (i)4485 5982 w 10 R f (from shrink-)1 502 1 4538 5962 t ( The)1 219(ing too quickly.)2 659 2 720 6082 t 10 I f (DTOL)1637 6082 w 10 R f (and)1932 6082 w 10 I f (d)2115 6082 w 10 S f (\260)2173 6082 w 10 R f (arrays provide a ``floor'' on the)5 1335 1 2252 6082 t 10 I f (d)3626 6082 w 7 I f (i)3687 6102 w 10 R f (values \320 some problems have)4 1286 1 3754 6082 t (points where)1 521 1 720 6202 t 10 S f (\357 \357)1 73 1 1274 6219 t 10 I f (J)1346 6202 w 7 I f (i)1401 6222 w 10 S f (\357 \357)1 73 1 1429 6219 t 10 R f (gets very small; when)3 898 1 1502 6202 t 10 S f (\357 \357)1 73 1 2433 6219 t 10 I f (J)2505 6202 w 7 I f (i)2560 6222 w 10 S f (\357 \357)1 73 1 2588 6219 t 10 R f ( often better to set)4 749(gets too small, it is)4 786 2 2661 6202 t 10 I f (d)4228 6202 w 7 I f (i)4289 6222 w 10 R f (to a larger value,)3 691 1 4349 6202 t 10 I f (d)720 6322 w 10 S f (\260)778 6322 w 7 I f (i)829 6342 w 10 R f (, than the floor value)4 829 1 857 6322 t 10 I f (DTOL)1711 6322 w 7 I f (i)1978 6342 w 10 R f (.)2006 6322 w (Occasionally it may be useful to set individual components of)9 2482 1 970 6478 t 10 I f (DTOL)3478 6478 w 10 R f (or)3760 6478 w 10 I f (d)3870 6478 w 10 S f (\260)3928 6478 w 10 R f ( do)1 127( To)1 163(to different values.)2 755 3 3995 6478 t ( call the)2 328( Next,)1 275( and set IV\(1\) to 13.)5 834(this, first call IVSET \(see \2472\), then set V\(DTINIT\) or V\(D0INIT\) to 0)12 2883 4 720 6598 t ( 14, meaning that it has only allo-)7 1393( it finds nothing wrong, it will return with IV\(1\) =)10 2057( if)1 117(optimization code:)1 753 4 720 6718 t ( from IV\(DTOL\) \320 see \2474d \320 where the)8 1721( determine)1 431( Now)1 251(cated storage \(within IV and V\).)5 1326 4 720 6838 t 10 I f (DTOL)4480 6838 w 10 R f (and)4767 6838 w 10 I f (d)4942 6838 w 10 S f (\260)5000 6838 w 10 R f ( you like to them \(making sure to assign)8 1709(arrays are located and assign whatever values)6 1888 2 720 6958 t 10 I f (all)4355 6958 w 10 R f (components\).)4499 6958 w ( algorithm will not further change)5 1351( \(The)1 238( will begin its algorithm.)4 987( it)1 106(Finally, call the optimization code again:)5 1638 5 720 7078 t (the)720 7198 w 10 I f (DTOL)867 7198 w 10 R f (and)1148 7198 w 10 I f (d)1317 7198 w 10 S f (\260)1375 7198 w 10 R f (arrays, but will use them in adaptively updating the scale vector)10 2549 1 1440 7198 t 10 I f (d)4014 7198 w 10 R f (by \(4.2\) and \(4.3\).\))3 759 1 4089 7198 t ( Optimization)1 2077( 5 -)2 133( -)1 1414(October 16, 1990)2 696 4 720 7680 t cleartomark showpage saveobj restore end %%PageBoundingBox: 61 8 514 764 %%EndPage: 5 6 %%Page: 6 7 %%PageBoundingBox: (atend) DpostDict begin /saveobj save def mark 7 pagesetup 10 R f (Optimization Usage Summary)2 1216 1 720 480 t 8 R f (PORT)4548 480 w 10 R f (library)4774 480 w 10 B f ( scaling for regression.)3 960(4b. Fixed)1 420 2 720 840 t 10 R f ( rather than adaptive scaling, in which case you sup-)9 2135(For regression problems, you may specify fixed)6 1935 2 970 996 t (ply your choice of values for the)6 1315 1 720 1116 t 10 I f (d)2063 1116 w 10 R f ( First)1 236( procedure analogous to that in the previous paragraph.)8 2214(vector by a)2 449 3 2141 1116 t ( IV\(DTYPE\) to 0, and IV\(1\) to 13, then call the optimization code)12 2718(call IVSET, then set V\(DINIT\) to \2611.0,)6 1602 2 720 1236 t ( from IV\(D\))2 497( you can determine)3 780( Now)1 250(and make sure it has set IV\(1\) to 14 \(i.e., has found nothing wrong\).)13 2793 4 720 1356 t (\(see \2474d\) where)2 650 1 720 1476 t 10 I f (d)1402 1476 w 10 R f ( to it; be sure to assign values to)8 1347(is stored and can assign the desired values)7 1732 2 1484 1476 t 10 I f (all)4596 1476 w 10 R f (compo-)4735 1476 w (nents of)1 319 1 720 1596 t 10 I f (d)1064 1596 w 10 R f ( will begin its algorithm.)4 987( it)1 106( call the optimization code again:)5 1329(. Finally,)1 384 4 1114 1596 t 10 B f ( scaling for general optimization)4 1377(4c. Adaptive)1 558 2 720 1836 t 10 R f (An adaptive choice of)3 911 1 970 1992 t 10 I f (d)1917 1992 w 10 R f ( such as MNH and MNHB that are explicitly)8 1888(is available only to routines)4 1149 2 2003 1992 t (given the Hessian matrix)3 996 1 720 2112 t 10 S f (\321)1741 2112 w 7 R f (2)1817 2072 w 10 I f (f)1876 2112 w 10 R f (\()1920 2112 w 10 I f (x)1961 2112 w 10 R f ( adaptive scaling update is similar to \(4.2\) and \(4.3\):)9 2089(\). The)1 263 2 2013 2112 t 10 I f (d)1305 2477 w 7 I f (i)1366 2497 w 10 R f (:)1435 2477 w 10 S f (=)1479 2477 w (\354)1591 2290 w (\357)1591 2390 w (\355)1591 2490 w (\357)1591 2590 w (\356)1591 2690 w 10 R f (max { V \( DFAC \))5 665 1 1640 2572 t (.)2321 2542 w 10 I f (d)2354 2572 w 7 I f (i)2415 2592 w 10 R f (,)2451 2572 w 10 I f (d)2517 2572 w 10 S f (\260)2567 2572 w 7 I f (i)2578 2592 w 10 R f (})2614 2572 w (max { V \( DFAC \))5 665 1 1640 2402 t (.)2321 2372 w 10 I f (d)2354 2402 w 7 I f (i)2415 2422 w 10 R f (,)2451 2402 w 10 S f (\357)2509 2419 w (\321)2557 2402 w 7 R f (2)2633 2362 w 10 I f (f)2692 2402 w 7 I f (ii)2731 2422 w 10 R f (\()2787 2402 w 10 I f (x)2828 2402 w 10 R f (\))2880 2402 w 10 S f (\357)2913 2419 w 7 R f (1)2974 2362 w 8 I f (/)3030 2362 w 7 R f (2)3073 2362 w 10 R f (})3124 2402 w (otherwise)3255 2572 w 7 R f (1)3648 2532 w 10 R f (if)3255 2402 w 10 S f (\357)3382 2419 w (\321)3430 2402 w 7 R f (2)3506 2362 w 10 I f (f)3565 2402 w 7 I f (ii)3604 2422 w 10 R f (\()3660 2402 w 10 I f (x)3701 2402 w 10 R f (\))3753 2402 w 10 S f (\357)3786 2419 w 7 R f (1)3847 2362 w 8 I f (/)3903 2362 w 7 R f (2)3946 2362 w 10 S f (\263)4030 2402 w 10 I f (DTOL)4126 2402 w 7 I f (i)4393 2422 w 10 I f (.)4429 2512 w 10 R f (To turn this updating on, you must set IV\(DTYPE\) to 1 or 2 and must set V\(DINIT\) to 0.0.)18 3639 1 720 2862 t 10 B f ( and V components that control scaling)6 1667(4d. IV)1 292 2 720 3102 t 10 R f (The IV and V components below appear in alphabetical order.)9 2488 1 970 3258 t 10 CW f (IV\(D\))1070 3498 w 10 R f ( is the subscript of V at which the)8 1343(\320 IV\(27\))1 421 2 1420 3498 t 10 I f (d)3209 3498 w 10 R f (\(scaling\) array starts [regression only].)4 1543 1 3284 3498 t 10 CW f (IV\(DTOL\))890 3678 w 10 R f ( is the subscript of V at which the)8 1367(\320 IV\(59\))1 421 2 1420 3678 t 10 I f (DTOL)3236 3678 w 10 R f (array starts, and IV\(DTOL\) +)4 1193 1 3521 3678 t 10 I f (p)4743 3678 w 10 R f (is the)1 218 1 4822 3678 t (subscript for V at which the)5 1127 1 1570 3798 t 10 I f (d)2725 3798 w 10 S f (\260)2783 3798 w 10 R f ( arrays are used in updating)5 1115( Both)1 248(array starts.)1 468 3 2851 3798 t 10 I f (d)4709 3798 w 10 R f (\320 see)1 254 1 4786 3798 t ( that)1 175(\2474a. \(Recall)1 507 2 1570 3918 t 10 I f (p)2277 3918 w 10 R f (is the number of)3 652 1 2352 3918 t 10 I f (p)3029 3918 w 10 R f (arameters, i.e., components in)3 1195 1 3079 3918 t 10 I f (x)4299 3918 w 10 R f (.\))4343 3918 w 10 CW f (IV\(DTYPE\))830 4098 w 10 R f ( tells whether)2 562(\320 IV\(16\))1 421 2 1420 4098 t 10 I f (d)2440 4098 w 10 R f (should be updated \(when updating is possible \320 some opti-)9 2513 1 2527 4098 t (mization codes disallow it and ignore IV\(DTYPE\)\).)6 2072 1 1570 4218 t (0 means do not update)4 899 1 1745 4338 t 10 I f (d)2669 4338 w 10 R f (.)2719 4338 w (1 means update)2 621 1 1745 4458 t 10 I f (d)2391 4458 w 10 R f (every iteration.)1 604 1 2466 4458 t (2 means update)2 633 1 1745 4578 t 10 I f (d)2409 4578 w 10 R f ( occasionally works better than)4 1270( This)1 235( iteration only.)2 600(on the first)2 445 4 2490 4578 t (IV\(DTYPE\) = 0.)2 674 1 1720 4698 t 10 I f (Default)1870 4818 w 10 R f (= 1 for regression, 0 for general optimization.)7 1822 1 2195 4818 t 10 CW f (V\(D0INIT\))830 4998 w 10 R f ( if positive, is the value to which the)8 1452(\320 V\(40\),)1 413 2 1420 4998 t 10 I f (d)3310 4998 w 10 S f (\260)3360 4998 w 10 R f (array used in updating)3 893 1 3426 4998 t 10 I f (d)4345 4998 w 10 R f (is initialized \320)2 619 1 4421 4998 t (see \2474a.)1 321 1 1570 5118 t 10 I f (Default)1870 5238 w 10 R f (= 1.0.)1 231 1 2195 5238 t 10 CW f (V\(DFAC\))950 5418 w 10 R f ( is used in updating)4 778(\320 V\(41\))1 388 2 1420 5418 t 10 I f (d)2611 5418 w 10 R f (\320 see \2474a.)2 446 1 2686 5418 t 10 I f (Default)1870 5538 w 10 R f (= 0.6.)1 231 1 2195 5538 t 10 CW f (V\(DINIT\))890 5718 w 10 R f ( initializes all)2 575( if nonnegative, is the value to which the optimization routine)10 2632(\320 V\(38\),)1 413 3 1420 5718 t (components of)1 592 1 1570 5838 t 10 I f (d)2188 5838 w 10 R f (before it does any updating of)5 1195 1 2263 5838 t 10 I f (d)3483 5838 w 10 R f ( V\(DINIT\))1 434(. If)1 141 2 3533 5838 t 10 S f (<)4133 5838 w 10 R f (0, then the optimiza-)3 827 1 4213 5838 t (tion routine will not initialize)4 1173 1 1570 5958 t 10 I f (d)2768 5958 w 10 R f (.)2818 5958 w 10 I f (Default)1870 6078 w 10 R f (= 0.0 for regression, \2611.0 for general optimization.)7 2022 1 2195 6078 t 10 CW f (V\(DTINIT\))830 6258 w 10 R f ( to which the optimization routine initializes all compo-)8 2259( if positive, is the value)5 948(\320 V\(39\),)1 413 3 1420 6258 t (nents of the)2 482 1 1570 6378 t 10 I f (DTOL)2085 6378 w 10 R f (array used in updating)3 914 1 2374 6378 t 10 I f (d)3321 6378 w 10 R f ( V\(DTINIT\))1 502( If)1 123(\320 see \2474a.)2 460 3 3403 6378 t 10 S f (\243)4520 6378 w 10 R f (0, then the)2 433 1 4607 6378 t (optimization routine will not initialize the)5 1670 1 1570 6498 t 10 I f (DTOL)3265 6498 w 10 R f (array.)3546 6498 w 10 I f (Default)1870 6618 w 10 R f (= 10)1 181 1 2195 6618 t 7 S f (-)2387 6578 w 7 R f (6)2437 6578 w 10 R f (.)2480 6618 w 8 S1 f (__________________)720 6980 w 8 R f ( 1984)1 180(1. The)1 224 2 720 7080 t 8 I f (Usage Summary)1 526 1 1144 7080 t 8 R f (omitted the factor of V\(DFAC\) here.)5 1171 1 1690 7080 t 10 R f ( 16, 1990)2 375( October)1 1702( 6 -)2 133(Optimization -)1 2110 4 720 7680 t cleartomark showpage saveobj restore end %%PageBoundingBox: 61 8 514 764 %%EndPage: 6 7 %%Page: 7 8 %%PageBoundingBox: (atend) DpostDict begin /saveobj save def mark 8 pagesetup 8 R f (PORT)720 480 w 10 R f ( Usage Summary)2 688(library Optimization)1 3406 2 946 480 t 10 B f ( tolerances)1 457(5. Stopping)1 510 2 720 840 t 10 R f ( optimization routines covered by this usage sum-)7 2032(The same stopping tests are available in all PORT)8 2038 2 970 996 t ( designed so you can say how close)7 1459( stopping tests are)3 740(mary. These)1 525 3 720 1116 t 10 I f (x)3475 1116 w 10 R f (should be to a local minimizer)5 1243 1 3550 1116 t 10 I f (x *)1 102 1 4824 1116 t 10 R f (or)4957 1116 w (how close)1 408 1 720 1236 t 10 I f (f)1159 1236 w 10 R f (\()1203 1236 w 10 I f (x)1244 1236 w 10 R f (\) should be to)3 565 1 1296 1236 t 10 I f (f)1892 1236 w 10 R f (\()1936 1236 w 10 I f (x *)1 102 1 1977 1236 t 10 R f ( default stopping)2 686( The)1 212( favorable ``convergence'' return occurs.)4 1662(\) before a)2 393 4 2087 1236 t ( strin-)1 239( This)1 231( misleading.)1 492(tolerances are stringent enough that such favorable convergence returns are seldom)10 3358 4 720 1356 t (gency may add little to the expense of minimizing)8 2028 1 720 1476 t 10 I f (f)2777 1476 w 10 R f (when)2834 1476 w 10 I f (f)3079 1476 w 10 R f (\()3123 1476 w 10 I f (x)3164 1476 w 10 R f (\) is evaluated accurately and when)5 1396 1 3216 1476 t 10 I f (x *)1 102 1 4641 1476 t 10 R f (is well)1 268 1 4772 1476 t ( if)1 92(defined. But)1 525 2 720 1596 t 10 I f (f)1368 1596 w 10 R f ( must solve a differential equation, do some numerical quadrature,)9 2693(is ``noisy'', e.g. if you)4 920 2 1427 1596 t (or perform an elaborate simulation to compute)6 1888 1 720 1716 t 10 I f (f)2638 1716 w 10 R f (\()2682 1716 w 10 I f (x)2723 1716 w 10 R f (\), then you will probably have to relax the default stop-)10 2265 1 2775 1716 t ( \2479 for more discussion of this matter.)7 1521( See)1 194(ping tolerances.)1 632 3 720 1836 t (In alphabetical order, the IV and V components controlling the stopping tests are:)12 3259 1 970 1992 t 10 CW f (IV\(MXFCAL\))770 2232 w 10 R f ( IV\(MXFCAL\))1 629( If)1 132( maximum number of function evaluations allowed.)6 2169( is the)2 269(\320 IV\(17\))1 421 5 1420 2232 t (evaluations of)1 564 1 1570 2352 t 10 I f (f)2160 2352 w 10 R f (\()2204 2352 w 10 I f (x)2245 2352 w 10 R f ( before another stopping test is satisfied, then you get a return)11 2463(\) occur)1 280 2 2297 2352 t (with IV\(1\) = 9.)3 605 1 1570 2472 t 10 I f (Default)1870 2592 w 10 R f (= 200.)1 256 1 2195 2592 t 10 CW f (IV\(MXITER\))770 2772 w 10 R f ( is generally one gradient)4 1013( \(There)1 315( is the maximum number of iterations allowed.)7 1871(\320 IV\(18\))1 421 4 1420 2772 t ( IV\(MXITER\) iterations occur before another stopping test)7 2366( If)1 117( iteration.\))1 417(evaluation per)1 570 4 1570 2892 t (is satisfied, then you get a return with IV\(1\) = 10.)10 1981 1 1570 3012 t 10 I f (Default)1870 3132 w 10 R f (= 150.)1 256 1 2195 3132 t 10 CW f (V\(AFCTOL\))830 3312 w 10 R f ( is the)2 271(\320 V\(31\))1 388 2 1420 3312 t 10 I f (absolute function-convergence)1 1244 1 2120 3312 t 10 R f ( 6 for)2 250( return with IV\(1\) =)4 857(tolerance. A)1 528 3 3405 3312 t (absolute function convergence occurs if)4 1626 1 1570 3432 t 10 S f (\357)3230 3449 w 10 I f (f)3286 3432 w 10 R f (\()3330 3432 w 10 I f (x)3371 3432 w 10 R f (\))3423 3432 w 10 S f (\357)3456 3449 w (<)3545 3432 w 10 R f ( of)1 116( test is only)3 486(V\(AFCTOL\). This)1 789 3 3649 3432 t (interest on problems where)3 1087 1 1570 3552 t 10 I f (f)2683 3552 w 10 R f (\()2727 3552 w 10 I f (x *)1 102 1 2768 3552 t 10 R f (\))2878 3552 w 10 S f (=)2968 3552 w 10 R f ( with artifi-)2 459(0 is possible, such as fitting problems)6 1509 2 3072 3552 t ( test described below fails when)5 1313( relative function convergence)3 1234( [The)1 246(cial \(exact\) data.)2 677 4 1570 3672 t (convergence to a)2 681 1 1570 3792 t 10 I f (f)2279 3792 w 10 R f (\()2323 3792 w 10 I f (x *)1 102 1 2364 3792 t 10 R f (\))2474 3792 w 10 S f (=)2564 3792 w 10 R f ( below fails)2 474(0 occurs, and the X-convergence test described)6 1898 2 2668 3792 t (when convergence to)2 863 1 1570 3912 t 10 I f (x *)1 102 1 2466 3912 t 10 S f (=)2617 3912 w 10 B f (0)2721 3912 w 10 R f (, i.e.,)1 205 1 2771 3912 t 10 I f (x)3009 3912 w 7 I f (i)3064 3932 w 10 I f (*)3080 3912 w 10 S f (=)3179 3912 w 10 R f (0 for all)2 332 1 3283 3912 t 10 I f (i)3648 3912 w 10 R f ( to construct)2 508( like)1 183( People)1 330(, occurs.)1 343 4 3676 3912 t (simple test examples having both)4 1333 1 1570 4032 t 10 I f (x *)1 102 1 2928 4032 t 10 S f (=)3079 4032 w 10 B f (0)3183 4032 w 10 R f (and)3258 4032 w 10 I f (f)3427 4032 w 10 R f (\()3471 4032 w 10 I f (x *)1 102 1 3512 4032 t 10 R f (\))3622 4032 w 10 S f (=)3712 4032 w 10 R f (0.])3816 4032 w 10 I f (Default)1870 4152 w 10 R f (= 10)1 181 1 2195 4152 t 7 S f (-)2387 4112 w 7 R f (20)2437 4112 w 10 R f (.)2515 4152 w 10 CW f (V\(LMAXS\))890 4332 w 10 R f ( is used in the singular-convergence test described below with V\(SCTOL\).)10 2981(\320 V\(36\))1 388 2 1420 4332 t 10 I f (Default)1870 4452 w 10 R f (= 1.0.)1 231 1 2195 4452 t 10 CW f (V\(RFCTOL\))830 4632 w 10 R f ( is the)2 257(\320 V\(32\))1 388 2 1420 4632 t 10 I f (relative function-convergence)1 1203 1 2099 4632 t 10 R f ( 4 \(or 5\))3 354( return with IV\(1\) =)4 829(tolerance. A)1 521 3 3336 4632 t (occurs if the algorithm thinks)4 1177 1 1570 4752 t 10 I f (f)2772 4752 w 10 R f (\()2816 4752 w 10 I f (x)2857 4752 w 10 R f (\))2909 4752 w 10 S f (-)2999 4752 w 10 I f (f)3111 4752 w 10 R f (\()3155 4752 w 10 I f (x *)1 102 1 3196 4752 t 10 R f (\))3306 4752 w 10 S f (\243)3388 4752 w 10 R f (V\(RFCTOL\))3484 4752 w (.)4014 4722 w 10 S f (\357)4039 4769 w 10 I f (f)4095 4752 w 10 R f (\()4139 4752 w 10 I f (x)4180 4752 w 10 R f (\))4232 4752 w 10 S f (\357)4265 4769 w 10 R f (.)4281 4752 w 10 I f (Default)1870 4872 w 10 R f ( { 10)2 164(= max)1 253 2 2195 4872 t 7 S f (-)2623 4832 w 7 R f (10)2673 4832 w 10 R f (, MACHEP)1 483 1 2759 4872 t 7 R f (2)3270 4832 w 8 I f (/)3326 4832 w 7 R f (3)3369 4832 w 10 R f (}.)3420 4872 w 10 CW f (V\(SCTOL\))890 5052 w 10 R f ( is the)2 241(\320 V\(37\))1 388 2 1420 5052 t 10 I f (singular-convergence)2075 5052 w 10 R f ( return with IV\(1\) = 7 occurs if a more)9 1556(tolerance. A)1 513 2 2971 5052 t (favorable stopping test is not satisfied and if the algorithm thinks)10 2599 1 1570 5172 t 10 I f (f)1832 5352 w 10 R f (\()1876 5352 w 10 I f (x)1917 5352 w 10 R f (\))1969 5352 w 10 S f (-)2059 5352 w 10 R f (min {)1 212 1 2163 5352 t 10 I f (f)2391 5352 w 10 R f (\()2435 5352 w 10 I f (y)2476 5352 w 10 R f (\) :)1 77 1 2528 5352 t 10 S f (\357 \357)1 73 1 2605 5369 t 10 I f (D)2677 5352 w 10 R f (\()2757 5352 w 10 I f (y)2798 5352 w 10 S f (-)2882 5352 w 10 I f (x)2977 5352 w 10 R f (\))3029 5352 w 10 S f (\357 \357)1 73 1 3062 5369 t (\243)3167 5352 w 10 R f ( })1 64(V \( LMAXS \))3 512 2 3230 5352 t 10 S f (<)3855 5352 w 10 R f (V \( SCTOL \))3 479 1 3959 5352 t (.)4454 5322 w 10 S f (\357)4479 5369 w 10 I f (f)4535 5352 w 10 R f (\()4579 5352 w 10 I f (x)4620 5352 w 10 R f (\))4672 5352 w 10 S f (\357)4705 5369 w 10 R f (,)4753 5352 w (where)1570 5532 w 10 I f (D)1844 5532 w 10 R f ( this test is satisfied, it appears that)7 1443( When)1 295( by \(4.1\).)2 380(is given)1 320 4 1947 5532 t 10 I f (x)4417 5532 w 10 R f (has too many)2 547 1 4493 5532 t (degrees of freedom \320 and you should ponder whether)8 2178 1 1570 5652 t 10 I f (f)3773 5652 w 10 R f (was properly formulated.)2 1006 1 3826 5652 t 10 I f (Default)1870 5772 w 10 R f ( { 10)2 164(= max)1 253 2 2195 5772 t 7 S f (-)2623 5732 w 7 R f (10)2673 5732 w 10 R f (, MACHEP)1 483 1 2759 5772 t 7 R f (2)3270 5732 w 8 I f (/)3326 5732 w 7 R f (3)3369 5732 w 10 R f (}.)3420 5772 w 10 CW f (V\(XCTOL\))890 5952 w 10 R f ( is the)2 265(\320 V\(33\))1 388 2 1420 5952 t 10 I f (X-convergence)2111 5952 w 10 R f ( 5\) occurs if the)4 682( return with IV\(1\) = 3 \(or)6 1087(tolerance. A)1 525 3 2746 5952 t ( from)1 225(algorithm thinks the scaled distance)4 1460 2 1570 6072 t 10 I f (x)3286 6072 w 10 R f (to)3361 6072 w 10 I f (x *)1 102 1 3470 6072 t 10 R f ( scaled)1 280( This)1 234(is at most V\(XCTOL\).)3 923 3 3603 6072 t (distance,)1570 6192 w 10 S f (r)1947 6192 w 10 R f (\()2010 6192 w 10 I f (x)2051 6192 w 10 R f (,)2103 6192 w 10 I f (x *)1 102 1 2160 6192 t 10 R f (\), is defined by)3 599 1 2270 6192 t 10 S f (r)1852 6432 w 10 R f (\()1915 6432 w 10 I f (x)1956 6432 w 10 R f (,)2008 6432 w 10 I f (y)2065 6432 w 10 R f (\) :)1 110 1 2117 6432 t 10 S f (=)2243 6432 w 10 R f (max {)1 228 1 2372 6502 t 10 I f (d)2608 6502 w 7 I f (j)2669 6522 w 10 R f (.)2705 6472 w (\()2738 6502 w 10 S f (\357)2771 6519 w 10 I f (x)2819 6502 w 7 I f (j)2874 6522 w 10 S f (\357)2902 6519 w (+)2991 6502 w (\357)3087 6519 w 10 I f (y)3135 6502 w 7 I f (j)3190 6522 w 10 S f (\357)3218 6519 w 10 R f ( 1)1 91(\) :)1 77 2 3266 6502 t 10 S f (\243)3475 6502 w 10 I f (j)3579 6502 w 10 S f (\243)3648 6502 w 10 I f (p)3744 6502 w 10 R f (})3802 6502 w (max {)1 228 1 2461 6352 t 10 I f (d)2697 6352 w 7 I f (i)2758 6372 w 10 R f (.)2794 6322 w 10 S f (\357)2819 6369 w 10 I f (x)2867 6352 w 7 I f (i)2922 6372 w 10 S f (-)2999 6352 w 10 I f (y)3103 6352 w 7 I f (i)3158 6372 w 10 S f (\357)3186 6369 w 10 R f (: 1)1 119 1 3234 6352 t 10 S f (\243)3394 6352 w 10 I f (i)3490 6352 w 10 S f (\243)3559 6352 w 10 I f (p)3655 6352 w 10 R f (})3713 6352 w 10 S1 f (_ ______________________________)1 1508 1 2357 6402 t 10 R f (, \(5.1\))1 1157 1 3883 6432 t (where)1570 6682 w 10 I f (d)1838 6682 w 10 R f (is the scale vector \(\2474\).)4 928 1 1913 6682 t 10 I f (Default)1870 6802 w 10 R f (= MACHEP)1 498 1 2195 6802 t 7 R f (1)2721 6762 w 8 I f (/)2777 6762 w 7 R f (2)2820 6762 w 10 R f (.)2863 6802 w ( like by supplying your own function RLDST)7 1874(You may change \(5.1\) to whatever you)6 1596 2 1570 6982 t (\(DRLDST in double precision\) to compute)5 1718 1 1570 7102 t 10 S f (r)3313 7102 w 10 R f (\()3376 7102 w 10 I f (x)3417 7102 w 10 R f (,)3469 7102 w 10 I f (y)3526 7102 w 10 R f ( RLDST should begin)3 881(\). Your)1 313 2 3578 7102 t ( Optimization)1 2077( 7 -)2 133( -)1 1414(October 16, 1990)2 696 4 720 7680 t cleartomark showpage saveobj restore end %%PageBoundingBox: 61 8 514 764 %%EndPage: 7 8 %%Page: 8 9 %%PageBoundingBox: (atend) DpostDict begin /saveobj save def mark 9 pagesetup 10 R f (Optimization Usage Summary)2 1216 1 720 480 t 8 R f (PORT)4548 480 w 10 R f (library)4774 480 w 10 CW f (REAL FUNCTION RLDST\(P, D, X, Y\))5 1860 1 1920 840 t (INTEGER P)1 540 1 1920 960 t (REAL D\(P\), X\(P\), Y\(P\))3 1260 1 1920 1080 t (V\(XFTOL\))890 1320 w 10 R f ( is the)2 263(\320 V\(34\))1 388 2 1420 1320 t 10 I f (false-convergence)2108 1320 w 10 R f ( return with IV\(1\) = 8 occurs if a more)9 1646(tolerance. A)1 524 2 2870 1320 t ( length at most)3 691(favorable stopping test is not satisfied and if a step of scaled)11 2779 2 1570 1440 t ( a)1 72( Such)1 253( length'' is in the sense of \(5.1\).)7 1287( ``Scaled)1 384(V\(XFTOL\) is tried but not accepted.)5 1474 5 1570 1560 t ( is an error in computing)5 1005(return generally means there)3 1153 2 1570 1680 t 10 S f (\321)3757 1680 w 10 I f (f)3844 1680 w 10 R f (\()3888 1680 w 10 I f (x)3929 1680 w 10 R f (\), or the favorable conver-)4 1059 1 3981 1680 t ( perhaps V\(AFCTOL\)\) are too tight)5 1478(gence tolerances \(V\(RFCTOL\), V\(XCTOL\), and)4 1992 2 1570 1800 t (for the accuracy to which)4 1017 1 1570 1920 t 10 I f (f)2613 1920 w 10 R f (\()2657 1920 w 10 I f (x)2698 1920 w 10 R f (\) is computed \(see \2479\), or)5 1025 1 2750 1920 t 10 S f (\321)3800 1920 w 10 I f (f)3887 1920 w 10 R f (\(or)3940 1920 w 10 I f (f)4081 1920 w 10 R f (itself\) is discontinuous)2 906 1 4134 1920 t (near)1570 2040 w 10 I f (x)1773 2040 w 10 R f ( error in computing)3 798(. An)1 204 2 1817 2040 t 10 S f (\321)2852 2040 w 10 I f (f)2939 2040 w 10 R f (\()2983 2040 w 10 I f (x)3024 2040 w 10 R f (\) usually leads to false convergence after only a)8 1964 1 3076 2040 t (few iterations \320 often in the first.)6 1362 1 1570 2160 t 10 I f (Default)1870 2280 w 10 R f (= 100)1 231 1 2195 2280 t (.)2434 2250 w (MACHEP.)2467 2280 w 10 B f ( output)1 309(6. Printed)1 447 2 720 2520 t 10 R f ( is IV\(PRUNIT\) = IV\(21\), the default for which is the standard)11 2611(The Fortran output unit for printing)5 1459 2 970 2676 t (output unit number \()3 825 1 720 2796 t 10 CW f (I1MACH\(2\))1545 2796 w 10 R f ( printing may be turned off by setting IV\(PRUNIT\) to 0.)10 2256(\). All)1 236 2 2085 2796 t 10 B f ( controls)1 369(6a. Print)1 397 2 720 3036 t 10 R f ( such printing is done by default.)6 1313( All)1 178(Several IV components determine what printing is done.)7 2258 3 970 3192 t 10 CW f (IV\(COVPRT\))770 3432 w 10 R f ( covariance matrix and regres-)4 1240( [regression routines only] controls printing of a)7 1959(\320 IV\(14\))1 421 3 1420 3432 t (sion diagnostic array:)2 860 1 1570 3552 t (0 means print neither.)3 871 1 1745 3672 t (1 means print just an estimated covariance matrix.)7 2008 1 1745 3792 t (2 means print just the diagnostic array.)6 1551 1 1745 3912 t (3 means print both.)3 772 1 1745 4032 t 10 I f (Default)1870 4152 w 10 R f (= 3.)1 156 1 2195 4152 t (If IV\(COVPRT\))1 661 1 1570 4332 t 10 S f (>)2261 4332 w 10 R f (0, and if the Hessian approximation used in computing the covari-)10 2694 1 2346 4332 t ( regression diagnostics is positive definite, then an upper bound on the)11 2880(ance matrix or)2 590 2 1570 4452 t (reciprocal of the Euclidean condition number \(i.e., an upper bound on the ratio of)13 3470 1 1570 4572 t ( If)1 124(smallest to largest eigenvalue\) of this Hessian approximation will also be printed.)11 3346 2 1570 4692 t ( \(say less than .01 or .001\), then you should regard the com-)12 2447(this number is very small)4 1023 2 1570 4812 t ( this case, if)3 705( In)1 209( with considerable skepticism.)3 1438(puted covariance matrix)2 1118 4 1570 4932 t 10 S f (\357)1570 5052 w 10 R f (IV\(COVREQ\))1619 5052 w 10 S f (\357)2201 5052 w 10 R f ( then you are probably ``close'' to singular conver-)8 2047(is 1 or 2 \(see \24710\))5 718 2 2275 5052 t ( routines that do the printing con-)6 1338( The)1 205( below for more discussion.)4 1107( \24710)1 176( See)1 195(gence \(\2475\).)1 449 6 1570 5172 t ( the PORT reference sheet for the relevant)7 1777(trolled by IV\(COVPRT\) are described in)5 1693 2 1570 5292 t (iteration driver.)1 621 1 1570 5412 t 10 CW f (IV\(DRADPR\))770 5592 w 10 R f ( only] controls printing of messages)5 1520( [routines for general linear constraints)5 1629(\320 IV\(101\))1 471 3 1420 5592 t (about constraints dropped and added:)4 1492 1 1570 5712 t (1 means print which constraints are dropped and added.)8 2226 1 1745 5832 t (0 means omit this printing.)4 1076 1 1745 5952 t 10 I f (Default)1870 6072 w 10 R f (= 1.)1 156 1 2195 6072 t ( let you specify both simple bounds \(1.1\))7 1687(Routines allowing general linear constraints)4 1783 2 1570 6252 t ( controlled by IV\(DRADPR\), the)4 1365( the printing)2 509( In)1 143(and general linear constraints \(1.2\).)4 1453 4 1570 6372 t 10 I f (i)1570 6492 w 10 R f (th simple lower bound constraint)4 1316 1 1598 6492 t 10 I f (x)2940 6492 w 7 I f (i)2995 6512 w 10 S f (\263)3064 6492 w 10 I f (b)3160 6492 w 10 S f (_)3158 6492 w 7 I f (i)3215 6511 w (x)3215 6452 w 10 R f (is denoted)1 409 1 3280 6492 t 10 I f (i)3715 6492 w 10 R f (, and the)2 343 1 3743 6492 t 10 I f (i)4112 6492 w 10 R f (th simple upper bound)3 900 1 4140 6492 t (constraint)1570 6618 w 10 I f (x)2008 6618 w 7 I f (i)2063 6638 w 10 S f (\243)2132 6618 w 10 I f (b)2228 6618 w 10 S1 f (_)2233 6525 w 7 I f (i)2283 6637 w (x)2283 6550 w 10 R f (is denoted)1 427 1 2366 6618 t 10 S f (-)2837 6618 w 10 I f (i)2908 6618 w 10 R f (; similarly, the)2 619 1 2936 6618 t 10 I f (i)3598 6618 w 10 R f (th general lower bound constraint)4 1414 1 3626 6618 t 7 I f (j)1572 6888 w 7 S f (=)1603 6888 w 7 R f (1)1653 6888 w 15 S f (S)1586 6818 w 7 I f (p)1613 6688 w 10 I f (C)1732 6788 w 7 I f (i)1810 6808 w 7 R f (,)1835 6808 w 7 I f (j)1864 6808 w 10 I f (x)1900 6788 w 7 I f (j)1955 6808 w 10 S f (\263)2024 6788 w 10 I f (b)2120 6788 w 10 S f (_)2118 6788 w 7 I f (i)2175 6807 w (c)2175 6748 w 10 R f (is denoted)1 461 1 2292 6788 t 10 I f (i)2831 6788 w 10 R f (G, and the)2 519 1 2859 6788 t 10 I f (i)3456 6788 w 10 R f ( bound constraint)2 802(th general upper)2 754 2 3484 6788 t 7 I f (j)1572 7138 w 7 S f (=)1603 7138 w 7 R f (1)1653 7138 w 15 S f (S)1586 7068 w 7 I f (p)1613 6938 w 10 I f (C)1732 7038 w 7 I f (i)1810 7058 w 7 R f (,)1835 7058 w 7 I f (j)1864 7058 w 10 I f (x)1900 7038 w 7 I f (j)1955 7058 w 10 S f (\243)2024 7038 w 10 I f (b)2120 7038 w 10 S1 f (_)2125 6945 w 7 I f (i)2175 7057 w (c)2175 6970 w 10 R f (is denoted)1 416 1 2248 7038 t 10 S f (-)2697 7038 w 10 I f (i)2768 7038 w 10 R f ( 2 means the second simple lower bound con-)8 1889(G. Thus)1 355 2 2796 7038 t (straint and \2613G means the third general upper bound constraint.)9 2546 1 1570 7238 t ( 16, 1990)2 375( October)1 1702( 8 -)2 133(Optimization -)1 2110 4 720 7680 t cleartomark showpage saveobj restore end %%PageBoundingBox: 61 8 514 764 %%EndPage: 8 9 %%Page: 9 10 %%PageBoundingBox: (atend) DpostDict begin /saveobj save def mark 10 pagesetup 8 R f (PORT)720 480 w 10 R f ( Usage Summary)2 688(library Optimization)1 3406 2 946 480 t ( controlled by)2 581(Subroutine DRADP \(DDRADP in double precision\) does the printing)8 2889 2 1570 840 t ( the source code for details.)5 1097(IV\(DRADPR\): see)1 782 2 1570 960 t 10 CW f (IV\(OUTLEV\))770 1140 w 10 R f ( IV\(OUTLEV\) is nonzero,)3 1109( If)1 133( iteration summary.)2 814( controls the printing of an)5 1143(\320 IV\(19\))1 421 5 1420 1140 t (then an iteration summary is printed every)6 2058 1 1570 1260 t 10 S f (\357)3714 1260 w 10 R f (IV\(OUTLEV\))3763 1260 w 10 S f (\357)4333 1260 w 10 R f (iterations. If)1 573 1 4467 1260 t ( IV\(OUTLEV\))1 599( For)1 193( then no iteration summary is printed.)6 1526(IV\(OUTLEV\) = 0,)2 757 4 1570 1380 t 10 S f (>)4674 1380 w 10 R f (0, long)1 282 1 4758 1380 t ( IV\(OUTLEV\))1 595(summary lines are printed, and for)5 1380 2 1570 1500 t 10 S f (<)3570 1500 w 10 R f (0, short summary lines are printed.)5 1390 1 3650 1500 t (See \2476b for details.)3 771 1 1570 1620 t 10 I f (Default)1870 1740 w 10 R f (= 1.)1 156 1 2195 1740 t ( in double precision\) does the printing controlled by)8 2220(Subroutine ITSUM \(DITSUM)2 1250 2 1570 1920 t ( \2476c.)1 194(IV\(OUTLEV\): see)1 775 2 1570 2040 t 10 CW f (IV\(PARPRT\))770 2220 w 10 R f ( few nondefault IV\) input components.)5 1568( controls printing of nondefault V \(and a)7 1631(\320 IV\(20\))1 421 3 1420 2220 t ( IV\(PARPRT\) = 0 suppresses this)5 1418(IV\(PARPRT\) = 1 causes them to be printed, and)8 2052 2 1570 2340 t (printing.)1570 2460 w 10 I f (Default)1870 2580 w 10 R f (= 1.)1 156 1 2195 2580 t ( controlled by)2 583(Subroutine PARCK \(DPARCK in double precision\) does the printing)8 2887 2 1570 2760 t ( \2476c.)1 194(IV\(PARPRT\): see)1 755 2 1570 2880 t 10 CW f (IV\(PRUNIT\))770 3060 w 10 R f ( which all printing \(other than error messages)7 1921( is the Fortran unit number on)6 1278(\320 IV\(21\))1 421 3 1420 3060 t ( can turn all)3 474( You)1 222( codes\) is done.)3 621(from the top-level PORT versions of the optimization)7 2153 4 1570 3180 t (this printing off at once by setting IV\(PRUNIT\) to 0.)9 2115 1 1570 3300 t 10 I f (Default)1870 3420 w 10 R f (=)2195 3420 w 10 I f (standard output unit)2 818 1 2276 3420 t 10 R f (=)3119 3420 w 10 CW f (I1MACH\(2\))3200 3420 w 10 R f (.)3740 3420 w 10 CW f (IV\(SOLPRT\))770 3600 w 10 R f ( controls printing of the returned)5 1311(\320 IV\(22\))1 421 2 1420 3600 t 10 I f (x)3179 3600 w 10 R f (, scale vector)2 527 1 3223 3600 t 10 I f (d)3777 3600 w 10 R f (, and \(except for routines with)5 1213 1 3827 3600 t (general linear constraints\) the gradient)4 1571 1 1570 3720 t 10 S f (\321)3175 3720 w 10 I f (f)3262 3720 w 10 R f (\()3306 3720 w 10 I f (x)3347 3720 w 10 R f ( this)1 178( = 1 means provide)4 802(\). IV\(SOLPRT\))1 661 3 3399 3720 t (printing, and IV\(SOLPRT\) = 0 means omit it.)7 1831 1 1570 3840 t 10 I f (Default)1870 3960 w 10 R f (= 1.)1 156 1 2195 3960 t ( controls printing of Lagrange multi-)5 1498(For general linear constraints, IV\(SOLPRT\) also)5 1972 2 1570 4140 t ( constraints \(1.1\) and \(1.2\) that are active or redundant at)10 2342(pliers and a list of the)5 903 2 1570 4260 t 10 I f (x)4847 4260 w 7 I f (final)4902 4220 w 10 R f (\(the returned)1 536 1 1570 4380 t 10 I f (x)2155 4380 w 10 R f ( constraints are those whose normals are linearly)7 2111(\). \(``Redundant'')1 730 2 2199 4380 t ( of the other active constraints.)5 1241(dependent on the normals)3 1038 2 1570 4500 t 10 I f (x)3901 4500 w 7 I f (final)3956 4460 w 10 R f (would satisfy the same)3 919 1 4121 4500 t ( constraints are those that the)5 1192( ``Active'')1 454(stopping test with these constraints removed.)5 1824 3 1570 4620 t (algorithm regards as equality constraints at)5 1832 1 1570 4740 t 10 I f (x)3450 4740 w 7 I f (final)3505 4700 w 10 R f ( as)1 130( constraints are denoted)3 1014(. The)1 253 3 3643 4740 t (explained above with IV\(DRADPR\); the signs of the multipliers are explained with)11 3470 1 1570 4860 t ( provide all this printing, and IV\(SOLPRT\))6 1748( = 1 means)3 448( IV\(SOLPRT\))1 598(IV\(AM\) in \24714.\))2 676 4 1570 4980 t ( the following procedure to)4 1091( use)1 184( control is also possible:)4 971( Finer)1 262( all of it.)3 342(= 0 means omit)3 620 6 1570 5100 t (request some but possibly not all of of this printing.)9 2067 1 1570 5220 t 10 S f (\267)1920 5400 w 10 R f (Set IV\(SOLPRT\) to 1.)3 900 1 1991 5400 t 10 S f (\267)1920 5520 w 10 R f ( want to have)3 544(If you)1 243 2 1993 5520 t 10 I f (x)2808 5520 w 7 I f (final)2863 5480 w 10 R f (and the returned scale vector)4 1158 1 3029 5520 t 10 I f (d)4215 5520 w 10 R f (printed, set)1 447 1 4293 5520 t (IV\(SOLPRT\) to IV\(SOLPRT\) + 1.)4 1397 1 1870 5640 t 10 S f (\267)1920 5760 w 10 R f ( to have the indices of the active or redundant constraints)10 2289(If you want)2 460 2 1991 5760 t (printed, set IV\(SOLPRT\) to IV\(SOLPRT\) + 2.)6 1866 1 1870 5880 t 10 S f (\267)1920 6000 w 10 R f ( to have the Lagrange multipliers printed, set)7 2142(If you want)2 558 2 2040 6000 t (IV\(SOLPRT\) to IV\(SOLPRT\) + 4.)4 1397 1 1870 6120 t ( 8 has the same effect as IV\(SOLPRT\) = 1, and)10 2018(Thus, for example, IV\(SOLPRT\) =)4 1452 2 1570 6300 t (IV\(SOLPRT\) = 4 causes printing of the Lagrange multipliers to be omitted.)11 3020 1 1570 6420 t ( ITSUM)1 346(Unless specified otherwise in the relevant PORT reference sheet, subroutine)9 3124 2 1570 6600 t ( \2476c.)1 194( see)1 177(\(DITSUM in double precision\) does the printing controlled by IV\(SOLPRT\):)9 3089 3 1570 6720 t 10 CW f (IV\(STATPR\))770 6900 w 10 R f ( print-)1 255( controls printing of a one-line convergence or error return message and)11 2944(\320 IV\(23\))1 421 3 1420 6900 t ( = \2611)2 220( IV\(STATPR\))1 601( test has been satisfied.)4 946(ing of summary statistics once a stopping)6 1703 4 1570 7020 t ( statistics;)1 407(suppresses all this printing; IV\(STATPR\) = 0 suppresses just the summary)10 3063 2 1570 7140 t (IV\(STATPR\) =)1 650 1 1570 7260 t 10 S f (-)2270 7260 w 10 I f (n)2341 7260 w 10 R f (causes printing of return messages only for IV\(1\))7 2140 1 2441 7260 t 10 S f (>)4631 7260 w 10 I f (n)4736 7260 w 10 R f (. The)1 254 1 4786 7260 t ( Optimization)1 2077( 9 -)2 133( -)1 1414(October 16, 1990)2 696 4 720 7680 t cleartomark showpage saveobj restore end %%PageBoundingBox: 61 8 514 764 %%EndPage: 9 10 %%Page: 10 11 %%PageBoundingBox: (atend) DpostDict begin /saveobj save def mark 11 pagesetup 10 R f (Optimization Usage Summary)2 1216 1 720 480 t 8 R f (PORT)4548 480 w 10 R f (library)4774 480 w (summary statistics include the final)4 1436 1 1570 840 t 10 I f (f)3037 840 w 10 R f (\()3081 840 w 10 I f (x)3122 840 w 10 R f (\), the RELDX, PRELDF, and NPRELDF val-)6 1866 1 3174 840 t ( the iteration summary \(\2476b\) for the final iteration \(even if printing of the iter-)14 3117(ues from)1 353 2 1570 960 t ( of function evaluations performed \(exclud-)5 1783(ation summary is turned off\), the number)6 1687 2 1570 1080 t ( for finite differences and for computing a covariance matrix or regression)11 3093(ing those)1 377 2 1570 1200 t (diagnostics\), the number of gradient evaluations performed \(or, for finite-difference)9 3470 1 1570 1320 t ( evaluations done to compute gradients \320)6 1807(gradients, the number of extra function)5 1663 2 1570 1440 t ( for computing a covariance matrix or regression diagnos-)8 2349(again excluding evaluations)2 1121 2 1570 1560 t ( done for com-)3 593(tics\), and the number of extra function and gradient evaluations \(if any\))11 2877 2 1570 1680 t (puting a covariance matrix or regression diagnostics.)6 2110 1 1570 1800 t 10 I f (Default)1870 1920 w 10 R f (= 1.)1 156 1 2195 1920 t ( in double precision\) does the printing controlled by)8 2220(Subroutine ITSUM \(DITSUM)2 1250 2 1570 2100 t ( \2476c.)1 194(IV\(STATPR\): see)1 749 2 1570 2220 t 10 CW f (IV\(X0PRT\))830 2400 w 10 R f ( controls printing of the initial)5 1228(\320 IV\(24\))1 421 2 1420 2400 t 10 I f (x)3099 2400 w 10 R f ( = 1 means provide this printing,)6 1339(. IV\(X0PRT\))1 558 2 3143 2400 t (and IV\(X0PRT\) = 0 means omit it.)6 1397 1 1570 2520 t 10 I f (Default)1870 2640 w 10 R f (= 1.)1 156 1 2195 2640 t ( in double precision\) does the printing controlled by)8 2220(Subroutine ITSUM \(DITSUM)2 1250 2 1570 2820 t ( \2476c.)1 194(IV\(X0PRT\): see)1 682 2 1570 2940 t 10 B f ( summary)1 430(6b. Iteration)1 558 2 720 3180 t 10 R f ( a long or a)4 461( Either)1 297( controlled by IV\(OUTLEV\) \320 see \2476a above.)7 1905(Printing of an iteration summary is)5 1407 4 970 3336 t ( two columns omitted.)3 901(short summary is possible; short summary lines are long summary lines with the last)13 3419 2 720 3456 t (Columns in the long iteration summary include:)6 1917 1 720 3576 t 10 CW f (IT)1250 3756 w 10 R f ( iteration number for this summary line.)6 1596(\320 the)1 272 2 1420 3756 t 10 CW f (NF)1250 3936 w 10 R f ( number of function evaluations \(computations of)6 1993(\320 the)1 272 2 1420 3936 t 10 I f (f)3713 3936 w 10 R f (\()3757 3936 w 10 I f (x)3798 3936 w 10 R f (\)\) so far computed, excluding)4 1190 1 3850 3936 t ( evaluations for finite)3 884( number of additional function)4 1261( The)1 215(those for finite differences.)3 1110 4 1570 4056 t (differences is reported only in the summary statistics controlled by IV\(STATPR\) \320)11 3470 1 1570 4176 t (see \2476a above and IV\(NGCALL\) in \24714.)6 1632 1 1570 4296 t 10 CW f (F)1310 4476 w 10 R f ( current value of)3 674(\320 the)1 272 2 1420 4476 t 10 I f (f)2397 4476 w 10 R f (\()2441 4476 w 10 I f (x)2482 4476 w 10 R f ( nonlinear least squares, this is)5 1251(\). For)1 253 2 2534 4476 t 10 I f (half)4069 4476 w 10 R f (of the residual sum)3 784 1 4256 4476 t (of squares at)2 504 1 1570 4596 t 10 I f (x)2099 4596 w 10 R f (.)2143 4596 w 10 CW f (RELDF)1070 4786 w 10 R f (\320 [)1 183 1 1420 4786 t 10 I f (f)1627 4786 w 10 R f (\()1671 4786 w 10 I f (x)1712 4786 w 7 I f (prev)1767 4746 w 10 R f (\))1907 4786 w 10 S f (-)1997 4786 w 10 I f (f)2109 4786 w 10 R f (\()2153 4786 w 10 I f (x)2194 4786 w 10 R f (\) ])1 74 1 2246 4786 t 13 I f (/)2360 4786 w 10 R f (max {)1 228 1 2428 4786 t 10 S f (\357)2656 4803 w 10 I f (f)2712 4786 w 10 R f (\()2756 4786 w 10 I f (x)2797 4786 w 7 I f (prev)2852 4746 w 10 R f (\))2992 4786 w 10 S f (\357)3025 4803 w 10 R f (,)3073 4786 w 10 S f (\357)3131 4803 w 10 I f (f)3187 4786 w 10 R f (\()3231 4786 w 10 I f (x)3272 4786 w 10 R f (\))3324 4786 w 10 S f (\357)3357 4803 w 10 R f ( relative function reduction)3 1333(}, the)1 302 2 3405 4786 t (achieved in the current iteration \(where)5 1600 1 1570 4906 t 10 I f (x)3201 4906 w 7 I f (prev)3256 4866 w 10 R f (is the)1 219 1 3418 4906 t 10 I f (x)3667 4906 w 10 R f (value from the end of the previ-)6 1299 1 3741 4906 t (ous iteration\).)1 555 1 1570 5026 t 10 CW f (PRELDF)1010 5206 w 10 R f ( value of RELDF that the algorithm predicted.)7 1848(\320 the)1 272 2 1420 5206 t 10 CW f (RELDX)1070 5386 w 10 R f (\320)1420 5386 w 10 S f (r)1570 5386 w 10 R f (\()1633 5386 w 10 I f (x)1674 5386 w 7 I f (prev)1729 5346 w 10 R f (,)1869 5386 w 10 I f (x)1935 5386 w 10 R f ( scaled length of the step taken in this iteration, where)10 2255(\), the)1 214 2 1987 5386 t 10 S f (r)4491 5386 w 10 R f (is given by)2 459 1 4581 5386 t (\(5.1\).)1570 5506 w 10 CW f (MODEL)1070 5686 w 10 R f ( ``G'')1 255( in the iteration:)3 639( routines only] the model or sequence of models used)9 2133(\320 [regression)1 593 4 1420 5686 t ( [1] for details on)4 749( See)1 208(means Gauss-Newton model, ``S'' means augmented model.)6 2513 3 1570 5806 t (these models.)1 544 1 1570 5926 t 10 CW f (STPPAR)1010 6106 w 10 R f ( means a)2 369( 0)1 109( \(e.g. Levenberg-Marquardt\) parameter for the step just taken:)8 2548(\320 step-length)1 594 4 1420 6106 t ( in)1 117(full Newton step, positive means a damped step, negative means a damped step)12 3353 2 1570 6226 t (which the special case described in [3] was detected.)8 2102 1 1570 6346 t 10 CW f (D)1020 6526 w 10 S f (*)1080 6526 w 10 CW f (STEP)1130 6526 w 10 R f (\320)1420 6526 w 10 S f (\357 \357)1 73 1 1570 6543 t 10 I f (D)1642 6526 w 10 R f (\()1722 6526 w 10 I f (x)1763 6526 w 10 S f (-)1856 6526 w 10 I f (x)1960 6526 w 7 I f (prev)2015 6486 w 10 R f (\))2155 6526 w 10 S f (\357 \357)1 73 1 2188 6543 t 10 R f (, where)1 293 1 2228 6526 t 10 I f (D)2546 6526 w 10 R f (is given by \(4.1\).)3 680 1 2643 6526 t 10 CW f (NPRELDF)950 6706 w 10 R f ( \(for NPRELDF)2 710( value of RELDF predicted for a full Newton step)9 2276(\320 the)1 272 3 1420 6706 t 10 S f (>)4736 6706 w 10 R f (0 or)1 191 1 4849 6706 t ( the quantity used in the relative function-)7 1855( is)1 119( This)1 255(NPRELDF = STPPAR = 0\).)4 1241 4 1570 6826 t ( NPRELDF)1 513( \2475.)1 168(convergence test described in)3 1228 3 1570 6946 t 10 S f (<)3522 6946 w 10 R f (0 means \261NPRELDF is the value)5 1420 1 3620 6946 t ( When)1 300( test \(\2475\).)2 404(against which V\(SCTOL\) is compared in the singular-convergence)7 2766 3 1570 7066 t (NPRELDF)1570 7186 w 10 S f (>)2041 7186 w 10 R f (0 and STPPAR)2 614 1 2122 7186 t 10 S f (\271)2762 7186 w 10 R f ( step\),)1 246(0 \(i.e., the algorithm does not take a full Newton)9 1951 2 2843 7186 t ( since PRELDF corresponds to the)5 1450(PRELDF will generally be less than NPRELDF,)6 2020 2 1570 7306 t ( 16, 1990)2 375( October)1 1677( 10 -)2 183(Optimization -)1 2085 4 720 7680 t cleartomark showpage saveobj restore end %%PageBoundingBox: 61 8 514 764 %%EndPage: 10 11 %%Page: 11 12 %%PageBoundingBox: (atend) DpostDict begin /saveobj save def mark 12 pagesetup 8 R f (PORT)720 480 w 10 R f ( Usage Summary)2 688(library Optimization)1 3406 2 946 480 t (step actually taken.)2 768 1 1570 840 t (Subroutine ITSUM \(DITSUM in double precision; see \2476c\) prints the iteration summary.)11 3569 1 720 1020 t 10 B f ( routine calling sequences)3 1092(6c. Print)1 391 2 720 1260 t 10 CW f (SUBROUTINE ITSUM\(D, G, IV, LIV, LV, P, V, X\))8 2640 1 1080 1416 t (INTEGER LIV, LV, P)3 1080 1 1080 1536 t (INTEGER IV\(LIV\))1 900 1 1080 1656 t (REAL D\(P\), G\(P\), V\(LV\), X\(P\))4 1680 1 1080 1776 t (SUBROUTINE PARCK\(KIND, D, IV, LIV, LV, P, V\))7 2640 1 1080 2016 t (INTEGER KIND, LIV, LV, P)4 1440 1 1080 2136 t (INTEGER IV\(LIV\))1 900 1 1080 2256 t (REAL D\(P\), V\(LV\))2 960 1 1080 2376 t 10 R f ( to ITSUM include)3 764(In addition to the ubiquitous IV and V \(and their lengths LIV and LV\), parameters)14 3306 2 970 2592 t ( gradient vector G =)4 852(the current scale vector D \(see \2474\), the problem dimension P \(see \2471a\), the current)14 3468 2 720 2712 t 10 S f (\321)720 2832 w 10 I f (f)807 2832 w 10 R f (\()851 2832 w 10 I f (x)892 2832 w 10 R f (\), and the current iterate X =)6 1133 1 944 2832 t 10 I f (x)2102 2832 w 10 R f (.)2146 2832 w ( 1 of \2472; the other parameters are the same as for)11 2101(Parameter KIND to PARCK comes from Table)6 1969 2 970 2988 t ( to optionally printing nondefault IV and V input components,)9 2614( addition)1 368( In)1 148(ITSUM \(omitting G and X\).)4 1190 4 720 3108 t ( in \24714\) and)3 513(PARCK initializes IV\(LASTIV\), IV\(LASTV\), IV\(NEXTIV\), and IV\(NEXTV\) \(all described)8 3807 2 720 3228 t (checks the validity of various inputs.)5 1471 1 720 3348 t 10 B f ( step bound)2 496(7. Initial)1 387 2 720 3588 t 10 R f (The algorithms maintain an estimate of the diameter of a region about the current)13 3260 1 970 3744 t 10 I f (x)4256 3744 w 10 R f (in which they can)3 713 1 4327 3744 t (predict the behavior of)3 945 1 720 3864 t 10 I f (f)1703 3864 w 10 R f ( region has the form {)5 942( This)1 241(reasonably well.)1 667 3 1769 3864 t 10 I f (y)3627 3864 w 10 R f (:)3679 3864 w 10 S f (\357 \357)1 73 1 3740 3881 t 10 I f (D)3812 3864 w 10 R f (\()3892 3864 w 10 I f (y)3933 3864 w 10 S f (-)4026 3864 w 10 I f (x)4130 3864 w 10 R f (\))4182 3864 w 10 S f (\357 \357)1 73 1 4215 3881 t (\243 d)1 145 1 4320 3864 t 10 R f (}, where)1 354 1 4473 3864 t 10 I f (D)4864 3864 w 10 R f (is)4973 3864 w ( initial)1 264( The)1 210(given by \(4.1\).)2 598 3 720 3984 t 10 S f (d)1822 3984 w 10 R f ( is given by V\(LMAX0\) =)5 1082(\(the one used at the start of the very first iteration\))10 2057 2 1901 3984 t (V\(35\), whose default value is 1.0.)5 1353 1 720 4104 t ( of the algorithms \320 different val-)6 1417(The choice of V\(LMAX0\) can profoundly affect the performance)8 2653 2 970 4260 t (ues sometimes lead to finding different local minimizers)7 2277 1 720 4380 t 10 I f (x *)1 102 1 3025 4380 t 10 R f ( of V\(LMAX0\))2 619( small or too large a value)6 1055(. Too)1 239 3 3127 4380 t (causes the algorithm to spend several function evaluations in the first iteration increasing or decreasing)14 4213 1 720 4500 t 10 S f (d)4966 4500 w 10 R f (.)5015 4500 w ( the first iteration \(the line with 1 in the IT column\) shows more)13 2608(If the iteration summary line \(see \2476b\) for)7 1712 2 720 4620 t ( the NF column\) then you would have saved some)9 2078(than one function evaluation performed \(the number in)7 2242 2 720 4740 t ( D)1 104(function evaluations had V\(LMAX0\) had the value in the)8 2360 2 720 4860 t 10 S f (*)3184 4860 w 10 R f ( If)1 123(STEP column of the same summary line.)6 1683 2 3234 4860 t ( iteration summary for the first)5 1259(you will be solving several similar problems, you may wish to examine the)12 3061 2 720 4980 t (problem and then choose an appropriate nondefault value for V\(LMAX0\) on the subsequent problems.)13 4103 1 720 5100 t 10 B f ( differences)1 490(8. Finite)1 375 2 720 5340 t 10 R f ( noisy functions \(\2479\),)3 861( For)1 191( V components affect various finite-difference computations.)6 2448(The following)1 570 4 970 5496 t (it may be necessary to relax the relevant component\(s\):)8 2206 1 720 5616 t 10 CW f (V\(DELTA0\))830 5796 w 10 R f ( computing a finite-)3 833( [regression routines only] helps choose the step sizes for)9 2399(\320 V\(44\))1 388 3 1420 5796 t ( gradient differences \(i.e., when IV\(COVREQ\))5 1887(difference Hessian approximation from)3 1583 2 1570 5916 t ( in computing a covariance matrix, regression diagnostics, or initial)9 2730(= 1 or 2\) for use)5 661 2 1570 6036 t 10 I f (S)4990 6036 w 10 R f ( differences involving)2 876( For)1 189(matrix \(\24717\).)1 527 3 1570 6156 t 10 I f (x)3187 6156 w 7 I f (i)3242 6176 w 10 R f (, step size)2 391 1 3270 6156 t (V \( DELTA 0 \))4 547 1 2478 6336 t (.)3041 6306 w (max {)1 228 1 3074 6336 t 10 S f (\357)3302 6353 w 10 I f (x)3350 6336 w 7 I f (i)3405 6356 w 10 S f (\357)3433 6353 w 10 R f (,)3481 6336 w 10 I f (d)3547 6336 w 7 I f (i)3602 6355 w 7 S f (-)3602 6296 w 7 R f (1)3652 6296 w 10 R f (})3703 6336 w (.)3759 6306 w (sign \()1 208 1 3792 6336 t 10 I f (x)4008 6336 w 7 I f (i)4063 6356 w 10 R f (\))4099 6336 w (is first tried.)2 486 1 1570 6516 t 10 I f (Default)1870 6636 w 10 R f (= MACHEP)1 498 1 2195 6636 t 7 R f (1)2721 6596 w 8 I f (/)2777 6596 w 7 R f (2)2820 6596 w 10 R f (.)2863 6636 w 10 CW f (V\(DLTFDC\))830 6816 w 10 R f ( computing a finite-)3 833( [regression routines only] helps choose the step sizes for)9 2399(\320 V\(42\))1 388 3 1420 6816 t ( \(i.e., when IV\(COVREQ\))3 1059(difference Hessian approximation from function differences)5 2411 2 1570 6936 t ( or initial)2 373(= \2611 or \2612\) for use in computing a covariance matrix, regression diagnostics,)12 3097 2 1570 7056 t 10 I f (S)1570 7176 w 10 R f ( differences involving)2 876( For)1 189(matrix \(\24717\).)1 527 3 1645 7176 t 10 I f (x)3262 7176 w 7 I f (i)3317 7196 w 10 R f (, step size)2 391 1 3345 7176 t ( Optimization)1 2052( 11 -)2 183( -)1 1389(October 16, 1990)2 696 4 720 7680 t cleartomark showpage saveobj restore end %%PageBoundingBox: 61 8 514 764 %%EndPage: 11 12 %%Page: 12 13 %%PageBoundingBox: (atend) DpostDict begin /saveobj save def mark 13 pagesetup 10 R f (Optimization Usage Summary)2 1216 1 720 480 t 8 R f (PORT)4548 480 w 10 R f (library)4774 480 w (V \( DLTFDC \))3 551 1 1816 840 t (.)2383 810 w (max {)1 228 1 2416 840 t 10 S f (\357)2644 857 w 10 I f (x)2692 840 w 7 I f (i)2747 860 w 10 S f (\357)2775 857 w 10 R f (,)2823 840 w 10 I f (d)2889 840 w 7 I f (i)2944 859 w 7 S f (-)2944 800 w 7 R f (1)2994 800 w 10 R f (})3045 840 w (is first tried.)2 486 1 1570 1020 t 10 I f (Default)1870 1140 w 10 R f (= MACHEP)1 498 1 2195 1140 t 7 R f (1)2721 1100 w 8 I f (/)2777 1100 w 7 R f (3)2820 1100 w 10 R f (.)2863 1140 w 10 CW f (V\(DLTFDJ\))830 1320 w 10 R f ( helps choose the step sizes for computing finite-)8 2121( [regression routines only])3 1111(\320 V\(43\))1 388 3 1420 1320 t ( differences involving)2 876( For)1 189(difference Jacobian approximations.)2 1449 3 1570 1440 t 10 I f (x)4109 1440 w 7 I f (i)4164 1460 w 10 R f (, step size)2 391 1 4192 1440 t (V \( DLTFDJ \))3 523 1 2680 1620 t (.)3219 1590 w (max {)1 228 1 3252 1620 t 10 S f (\357)3480 1637 w 10 I f (x)3528 1620 w 7 I f (i)3583 1640 w 10 S f (\357)3611 1637 w 10 R f (,)3659 1620 w 10 I f (d)3725 1620 w 7 I f (i)3780 1639 w 7 S f (-)3780 1580 w 7 R f (1)3830 1580 w 10 R f (})3881 1620 w (is first tried.)2 486 1 1570 1800 t 10 I f (Default)1870 1920 w 10 R f (= MACHEP)1 498 1 2195 1920 t 7 R f (1)2721 1880 w 8 I f (/)2777 1880 w 7 R f (2)2820 1880 w 10 R f (.)2863 1920 w 10 CW f (V\(ETA0\))950 2100 w 10 R f ( choose the step sizes for computing finite-)7 1822( [general optimization only] helps)4 1410(\320 V\(42\))1 388 3 1420 2100 t ( set V\(ETA0\) to your best guess at a)8 1501( should)1 299( You)1 229(difference gradient approximations.)2 1441 4 1570 2220 t (bound on the relative error in the computed values of)9 2166 1 1570 2340 t 10 I f (f)3767 2340 w 10 R f (\()3811 2340 w 10 I f (x)3852 2340 w 10 R f ( should be such)3 637(\): V\(ETA0\))1 499 2 3904 2340 t (that if)1 304 1 1570 2465 t 10 I f (f)1967 2465 w 11 R f (\304)1968 2435 w 10 R f (\()2011 2465 w 10 I f (x)2052 2465 w 10 R f ( value computed, then the true value)6 1852(\) is the)2 408 2 2104 2465 t 10 I f (f)4456 2465 w 10 R f (\()4500 2465 w 10 I f (x)4541 2465 w 10 R f (\) satisfies)1 447 1 4593 2465 t 10 I f (f)1570 2590 w 10 R f (\()1614 2590 w 10 I f (x)1655 2590 w 10 R f (\))1707 2590 w 10 S f (=)1797 2590 w 10 I f (f)1909 2590 w 11 R f (\304)1910 2560 w 10 R f (\()1953 2590 w 10 I f (x)1994 2590 w 10 R f (\))2046 2590 w (.)2095 2560 w (\( 1)1 91 1 2128 2590 t 10 S f (+ e)1 148 1 2268 2590 t 10 R f (\), where)1 328 1 2424 2590 t 10 S f (\357)2779 2607 w (e)2827 2590 w (\357)2871 2607 w (\243)2952 2590 w 10 I f (V)3048 2590 w 10 R f (\()3117 2590 w 10 I f (ETA)3158 2590 w 10 R f ( scheme used is a slight modifica-)6 1372( The)1 208(0 \).)1 116 3 3344 2590 t ( [4] for details.)3 593( See)1 194(tion of one proposed by Stewart [6].)6 1445 3 1570 2710 t 10 I f (Default)1870 2830 w 10 R f (= 10)1 181 1 2195 2830 t 7 R f (3)2381 2790 w 10 R f (.)2432 2800 w (MACHEP.)2465 2830 w ( of the finite-difference routines multiply the)6 1864( Some)1 291(The phrase ``first tried'' deserves explanation.)5 1915 3 970 2986 t (step size by .5 or \261.5 and try again if the first step they try is rejected \(\24711\).)17 3006 1 720 3106 t 10 B f ( functions)1 420(9. Noisy)1 364 2 720 3346 t 10 R f (Sometimes evaluating)1 897 1 970 3502 t 10 I f (f)1903 3502 w 10 R f (\()1947 3502 w 10 I f (x)1988 3502 w 10 R f ( computation, such as performing a simulation or)7 2049(\) involves an extensive)3 951 2 2040 3502 t ( such cases the)3 608( In)1 139( or integrating an ordinary or partial differential equation.)8 2346(adaptive numerical quadrature)2 1227 4 720 3622 t (value computed for)2 776 1 720 3747 t 10 I f (f)1521 3747 w 10 R f (\()1565 3747 w 10 I f (x)1606 3747 w 10 R f (\), say)1 216 1 1658 3747 t 10 I f (f)1899 3747 w 11 R f (\304)1900 3717 w 10 R f (\()1943 3747 w 10 I f (x)1984 3747 w 10 R f ( involve substantial error \(in the eyes of the optimization algorithm\).)10 2749(\), may)1 255 2 2036 3747 t (To eliminate some ``false convergence'' messages and useless function evaluations, it is necessary to)13 4320 1 720 3867 t ( increase)1 355(increase the stopping tolerances and, when finite-difference derivative approximations are used, to)11 3965 2 720 3987 t (the step-sizes used in estimating derivatives.)5 1776 1 720 4107 t ( have a good estimate)4 885(Intelligently choosing these tolerances requires you to)6 2182 2 970 4263 t 10 S f (h)4067 4263 w 10 R f (of the maximum rela-)3 883 1 4157 4263 t (tive error in)2 471 1 720 4388 t 10 I f (f)1216 4388 w 11 R f (\304)1217 4358 w 10 R f (\()1260 4388 w 10 I f (x)1301 4388 w 10 R f (\), i.e., of)2 338 1 1353 4388 t 10 S f (h)1716 4388 w 10 R f (such that)1 358 1 1801 4388 t 10 S f (\357)2329 4590 w 10 I f (f)2385 4573 w 11 R f (\304)2386 4543 w 10 R f (\()2429 4573 w 10 I f (x)2470 4573 w 10 R f (\))2522 4573 w 10 S f (-)2612 4573 w 10 I f (f)2724 4573 w 10 R f (\()2768 4573 w 10 I f (x)2809 4573 w 10 R f (\))2861 4573 w 10 S f (\357)2894 4590 w (\243 h)1 156 1 2975 4573 t (\357)3131 4590 w 10 I f (f)3187 4573 w 11 R f (\304)3188 4543 w 10 R f (\()3231 4573 w 10 I f (x)3272 4573 w 10 R f (\))3324 4573 w 10 S f (\357)3357 4590 w 10 I f (.)3405 4573 w 10 R f (\(9.1\))4849 4573 w (Often)720 4758 w 10 S f (h)973 4758 w 10 R f (is an input to the procedure that computes)7 1680 1 1059 4758 t 10 I f (f)2765 4758 w 11 R f (\304)2766 4728 w 10 R f (\()2809 4758 w 10 I f (x)2850 4758 w 10 R f ( other times estimating)3 917(\). At)1 209 2 2902 4758 t 10 S f (h)4054 4758 w 10 R f ( difficult;)1 377(may be more)2 523 2 4140 4758 t (see \2478.5 of [5] for more discussion.)6 1414 1 720 4878 t (Once you have an approximate)4 1397 1 970 5034 t 10 S f (h)2431 5034 w 10 R f ( tolerances V\(RFCTOL\) and)3 1265(, try setting the convergence)4 1284 2 2491 5034 t (V\(SCTOL\) as follows:)2 916 1 720 5154 t (V \( RFCTOL \))3 546 1 1220 5334 t 10 S f (=)1823 5334 w 10 R f ( :)1 77(V \( 32 \))3 262 2 1927 5334 t 10 S f (= h)1 164 1 2282 5334 t 10 I f (or)2487 5334 w 10 R f (10)2617 5334 w 10 S f (h)2725 5334 w 10 R f (,)2793 5334 w (V \( SCTOL \))3 479 1 1287 5514 t 10 S f (=)1823 5514 w 10 R f ( :)1 77(V \( 37 \))3 262 2 1927 5514 t 10 S f (= h)1 164 1 2282 5514 t 10 I f (.)2454 5514 w 10 R f ( requesting finite-difference derivative approximations \(\2478\), try using)7 2806(If you are)2 393 2 720 5694 t 10 S f (h)3948 5694 w 7 R f (1)4036 5654 w 8 I f (/)4092 5654 w 7 R f (2)4135 5654 w 10 R f (for V\(DELTA0\) and)2 833 1 4207 5694 t (V\(DLTFDJ\),)720 5814 w 10 S f (h)1269 5814 w 7 R f (1)1357 5774 w 8 I f (/)1413 5774 w 7 R f (3)1456 5774 w 10 R f (for V\(DLTFDC\), or)2 801 1 1524 5814 t 10 S f (h)2350 5814 w 10 R f (for V\(ETA0\), as appropriate.)3 1160 1 2435 5814 t (When you can specify)3 904 1 970 5970 t 10 S f (h)1905 5970 w 10 R f (, perhaps as an accuracy tolerance to an integration routine, you will gener-)12 3075 1 1965 5970 t ( make)1 246(ally find that the smaller you)5 1182 2 720 6095 t 10 S f (h)2178 6095 w 10 R f (, the more expensive)3 841 1 2238 6095 t 10 I f (f)3109 6095 w 11 R f (\304)3110 6065 w 10 R f (\()3153 6095 w 10 I f (x)3194 6095 w 10 R f ( this case you can reduce)5 1019( In)1 138(\) is to compute.)3 637 3 3246 6095 t (the cost of computing)3 902 1 720 6220 t 10 I f (f)1658 6220 w 11 R f (\304)1659 6190 w 10 R f (\()1702 6220 w 10 I f (x)1743 6220 w 10 R f ( happy.)1 306(\) by requesting only enough accuracy to make the optimization routine)10 2939 2 1795 6220 t ( \( F 0 \))4 204( algorithm predicts V)3 876(You can see from V\(PREDUC\) = V\(7\) what the)8 1996 3 720 6340 t 10 S f (-)3853 6340 w 10 I f (f)3965 6340 w 10 R f (\()4009 6340 w 10 I f (x)4050 6340 w 10 R f (\) to be, where V\(F0\) =)5 938 1 4102 6340 t (V\(13\) is the value)3 751 1 720 6460 t 10 I f (f)1507 6460 w 10 R f (\()1551 6460 w 10 I f (x)1592 6460 w 10 R f (\) had at the start of the iteration, and you will often find it satisfactory to specify)16 3396 1 1644 6460 t 10 S f (h =)1 164 1 720 6580 t 10 R f (10)933 6580 w 7 S f (-)1044 6540 w 7 R f (2)1094 6540 w 10 R f (.)1169 6550 w (V \( PREDUC \))3 557 1 1226 6580 t 12 I f (/)1823 6580 w 10 R f ( even)1 245( or perhaps)2 509(V \( F 0 \))4 276 3 1889 6580 t 10 S f (h =)1 164 1 2976 6580 t 10 R f (10)3189 6580 w 7 S f (-)3300 6540 w 7 R f (1)3350 6540 w 10 R f (.)3425 6550 w (V \( PREDUC \))3 557 1 3482 6580 t 12 I f (/)4079 6580 w 10 R f ( using)1 274( When)1 320(V \( F 0 \).)4 301 3 4145 6580 t ( should probably not tinker with)5 1351(finite-difference derivative approximations, you)3 1954 2 720 6700 t 10 S f (h)4063 6700 w 10 R f ( for)1 154( And)1 235(in this way.)2 490 3 4161 6700 t ( IV\(MODE\))1 491( if)1 112(regression routines, you should first check IV\(MODE\) = IV\(35\):)8 2595 3 720 6820 t 10 S f (>)3944 6820 w 10 R f ( finite-difference)1 672(0, then a)2 343 2 4025 6820 t ( provide accuracy consistent with V\(DELTA0\) [or)6 2143(Hessian computation is under way, and you should)7 2177 2 720 6940 t (V\(DLTFDC\)] \320 see \2478.)3 987 1 720 7060 t ( to IV and V \(for tinkering with)7 1409(Gaining access)1 621 2 970 7216 t 10 S f (h)3046 7216 w 10 R f (as in the previous paragraph\) deserves some)6 1888 1 3152 7216 t ( 16, 1990)2 375( October)1 1677( 12 -)2 183(Optimization -)1 2085 4 720 7680 t cleartomark showpage saveobj restore end %%PageBoundingBox: 61 8 514 764 %%EndPage: 12 13 %%Page: 13 14 %%PageBoundingBox: (atend) DpostDict begin /saveobj save def mark 14 pagesetup 8 R f (PORT)720 480 w 10 R f ( Usage Summary)2 688(library Optimization)1 3406 2 946 480 t ( you call a reverse-communication driver \(\2471c\), then you have immediate access to IV and V)15 3758(discussion. If)1 562 2 720 840 t (whenever the driver requests a new)5 1429 1 720 960 t 10 I f (f)2178 960 w 10 R f (\()2222 960 w 10 I f (x)2263 960 w 10 R f ( you call a forward-communication optimization routine,)6 2302( If)1 120(\) value.)1 303 3 2315 960 t (then you must provide a subroutine, say CALCF, to compute either)10 2723 1 720 1080 t 10 I f (f)3471 1080 w 10 R f (\()3515 1080 w 10 I f (x)3556 1080 w 10 R f (\) itself \(for general optimization\) or)5 1432 1 3608 1080 t (the information needed to compute)4 1398 1 720 1200 t 10 I f (f)2143 1200 w 10 R f (\()2187 1200 w 10 I f (x)2228 1200 w 10 R f ( either case the parameters to both the optimiza-)8 1926( In)1 134(\) \(for regression\).)2 700 3 2280 1200 t ( CALCF include ``user'' integer and floating-point arrays UI and UR; you could pass IV for)15 3685(tion routine and)2 635 2 720 1320 t (UI and V for UR, or you could put IV and V into a common block that CALCF knows about.)19 3733 1 720 1440 t 10 B f ( regression diagnostics, and confidence intervals)5 2050(10. Covariance,)1 688 2 720 1680 t 10 BI f (CAVEAT:)970 1836 w 10 I f ( be)1 138(An estimated covariance matrix and the confidence intervals derived from it may)11 3435 2 1467 1836 t ( the discussion of confi-)4 986( See)1 197( the assumptions behind the covariance computation are invalid.)8 2662(worthless if)1 475 4 720 1956 t (dence intervals below.)2 896 1 720 2076 t 10 R f ( matrix)1 289(Regression routines may offer an estimated covariance)6 2201 2 970 2232 t 10 S f (X)3488 2232 w 10 R f (and regression diagnostic vector)3 1298 1 3581 2232 t 10 I f (RD)4907 2232 w 10 R f (at the computed solution)3 992 1 720 2352 t 10 I f (x)1739 2352 w 7 I f (final)1794 2312 w 10 R f (, but only for favorable returns \(3)6 1345 1 1932 2352 t 10 S f (\243)3304 2352 w 10 R f (IV\(1\))3386 2352 w 10 S f (\243)3634 2352 w 10 R f ( The)1 206(6 \320 see \2473\).)3 516 2 3716 2352 t 10 I f (i)4464 2352 w 10 R f (th component)1 548 1 4492 2352 t (of)720 2472 w 10 I f (RD)839 2472 w 10 R f (is an estimate of the square-root of twice the relative)9 2206 1 1009 2472 t 7 R f (2)3220 2432 w 10 R f (\(or, if)1 239 1 3300 2472 t 10 I f (f)3576 2472 w 10 R f (\()3620 2472 w 10 I f (x)3661 2472 w 7 I f (final)3716 2432 w 10 R f (\))3862 2472 w 10 S f (=)3952 2472 w 10 R f (0, absolute\) change that)3 984 1 4056 2472 t (would occur in)2 603 1 720 2592 t 10 I f (f)1350 2592 w 10 R f (\()1394 2592 w 10 I f (x)1435 2592 w 7 I f (final)1490 2552 w 10 R f (\) if the)2 270 1 1636 2592 t 10 I f (i)1933 2592 w 10 R f ( may wish to take a closer look at the obser-)10 1768(th observation were deleted; you)4 1311 2 1961 2592 t (vations corresponding to large components of)5 1828 1 720 2712 t 10 I f (RD)2573 2712 w 10 R f ( used in defining the)4 820( of the square-root)3 734(. \(Because)1 440 3 2706 2712 t 10 I f (RD)4726 2712 w 10 R f (val-)4885 2712 w ( component)1 469(ues, if deleting)2 593 2 720 2832 t 10 I f (i)1807 2832 w 10 R f (would cause)1 496 1 1860 2832 t 10 S f (a)2381 2832 w 10 R f (times the estimated change in)4 1182 1 2469 2832 t 10 I f (x)3676 2832 w 7 I f (final)3731 2792 w 10 R f (as deleting component)2 899 1 3894 2832 t 10 I f (j)4818 2832 w 10 R f (, and)1 194 1 4846 2832 t ( the same direction, then)4 991(if both changes were in)4 939 2 720 2952 t 10 I f (RD)2678 2952 w 10 R f (\()2819 2952 w 10 I f (i)2860 2952 w 10 R f (\))2896 2952 w 10 S f (=)2986 2952 w (\357)3082 2969 w (a)3130 2952 w (\357)3193 2969 w 10 I f (RD)3241 2952 w 10 R f (\()3382 2952 w 10 I f (j)3439 2952 w 10 R f ( following IV components con-)4 1266(\).\) The)1 299 2 3475 2952 t (trol whether and how)3 851 1 720 3072 t 10 S f (X)1596 3072 w 10 R f (and)1686 3072 w 10 I f (RD)1855 3072 w 10 R f (are computed:)1 568 1 2013 3072 t 10 CW f (IV\(COVREQ\))770 3312 w 10 R f ( tells what kind of Hessian approximation)6 1743(\320 IV\(15\))1 421 2 1420 3312 t 10 I f (H)3621 3312 w 10 R f ( used in the computa-)4 912(should be)1 398 2 3730 3312 t (tions:)1570 3432 w ( and 2 request a finite-difference)5 1358(0, 1)1 161 2 1845 3552 t 10 I f (H)3401 3552 w 10 R f (computed from gradient differ-)3 1280 1 3510 3552 t (ences.)1820 3672 w (\2611 and \2612 request a finite-difference)5 1508 1 1845 3792 t 10 I f (H)3391 3792 w 10 R f (computed from function differ-)3 1289 1 3501 3792 t (ences.)1820 3912 w (3 and \2613 request)3 657 1 1845 4032 t 10 I f (H)2527 4032 w 10 S f (=)2648 4032 w 10 I f (J)2752 4032 w 7 I f (T)2801 3992 w 10 I f (J)2856 4032 w 10 R f (, where)1 293 1 2900 4032 t 10 I f (J)3218 4032 w 10 R f (is the Jacobian matrix at)4 971 1 3287 4032 t 10 I f (x)4283 4032 w 7 I f (final)4338 3992 w 10 R f (.)4476 4032 w (For nonlinear least-squares,)2 1120 1 1570 4152 t 10 S f (\357)2723 4152 w 10 R f (IV\(COVREQ\))2772 4152 w 10 S f (\357 \243)1 137 1 3354 4152 t 10 R f (1 requests a covariance matrix of the)6 1516 1 3524 4152 t (form)1570 4272 w 10 S f (X = s)2 278 1 2863 4452 t 7 R f (2)3146 4412 w 10 I f (H)3197 4452 w 7 S f (-)3280 4412 w 7 R f (1)3330 4412 w 10 I f (J)3381 4452 w 7 I f (T)3430 4412 w 10 I f (J H)1 124 1 3485 4452 t 7 S f (-)3620 4412 w 7 R f (1)3670 4412 w 10 R f (,)3721 4452 w 10 S f (\357)1570 4632 w 10 R f (IV\(COVREQ\))1619 4632 w 10 S f (\357)2201 4632 w 10 R f (= 2 requests a covariance matrix of the form)8 1768 1 2275 4632 t 10 S f (X = s)2 278 1 3033 4812 t 7 R f (2)3316 4772 w 10 I f (H)3367 4812 w 7 S f (-)3450 4772 w 7 R f (1)3500 4772 w 10 R f (,)3551 4812 w (and)1570 4992 w 10 S f (\357)1739 4992 w 10 R f (IV\(COVREQ\))1788 4992 w 10 S f (\357 \263)1 129 1 2370 4992 t 10 R f (3 requests a covariance matrix of the form)7 1687 1 2524 4992 t 10 S f (X = s)2 278 1 2954 5172 t 7 R f (2)3237 5132 w 10 R f (\()3288 5172 w 10 I f (J)3329 5172 w 7 I f (T)3378 5132 w 10 I f (J)3433 5172 w 10 R f (\))3485 5172 w 7 S f (-)3529 5132 w 7 R f (1)3579 5132 w 10 R f (,)3630 5172 w (where)1570 5352 w 10 S f (s)1840 5352 w 7 R f (2)1905 5312 w 10 R f ( { 1 ,)3 147( by max)2 328(is the residual sum of squares divided)6 1516 3 1975 5352 t 10 I f (n)4007 5352 w 10 S f (-)4097 5352 w 10 I f (p)4192 5352 w 10 R f (},)4250 5352 w 10 I f (n)4351 5352 w 10 R f (being the num-)2 611 1 4429 5352 t (ber of observations.)2 808 1 1570 5472 t 10 S f (\357)2437 5472 w 10 R f (IV\(COVREQ\))2486 5472 w 10 S f (\357)3068 5472 w 10 R f ( perhaps the most defensible choice, but)6 1648(= 1 is)2 241 2 3151 5472 t (the others have their proponents.)4 1306 1 1570 5592 t 10 I f (Default)1870 5712 w 10 R f (= 1.)1 156 1 2195 5712 t 10 CW f (IV\(RDREQ\))830 5892 w 10 R f ( tells whether to compute a covariance matrix or regression diagnostic array:)11 3057(\320 IV\(57\))1 421 2 1420 5892 t (0 means compute neither;)3 1029 1 1745 6012 t (1 means compute just a covariance matrix;)6 1708 1 1745 6132 t (2 means compute just the regression diagnostic array;)7 2144 1 1745 6252 t (3 means compute both.)3 927 1 1745 6372 t 10 I f (Default)1870 6492 w 10 R f (= 3.)1 156 1 2195 6492 t (Printing of)1 431 1 720 6672 t 10 S f (X)1176 6672 w 10 R f (and)1266 6672 w 10 I f (RD)1435 6672 w 10 R f ( their numerical values by looking at the appropri-)8 2016( can obtain)2 438( You)1 222(is described in \2476a.)3 771 4 1593 6672 t (ate IV and V components:)4 1048 1 720 6792 t 8 S1 f (__________________)720 6892 w 8 R f ( 1984)1 186(2. The)1 230 2 720 6992 t 8 I f (Usage Summary)1 532 1 1162 6992 t 8 R f ( remove dependence on the scale of)6 1176( To)1 136(omitted ``square-root of twice'' here.)4 1210 3 1721 6992 t 8 I f (f)4270 6992 w 8 R f (, ``relative'')1 388 1 4292 6992 t (was added in October, 1990.)4 912 1 720 7092 t 10 R f ( Optimization)1 2052( 13 -)2 183( -)1 1389(October 16, 1990)2 696 4 720 7680 t cleartomark showpage saveobj restore end %%PageBoundingBox: 61 8 514 764 %%EndPage: 13 14 %%Page: 14 15 %%PageBoundingBox: (atend) DpostDict begin /saveobj save def mark 15 pagesetup 10 R f (Optimization Usage Summary)2 1216 1 720 480 t 8 R f (PORT)4548 480 w 10 R f (library)4774 480 w 10 CW f (IV\(COVMAT\))770 840 w 10 R f ( triangle of)2 454( if positive, is the starting subscript in V for the lower)11 2220(\320 IV\(26\),)1 446 3 1420 840 t 10 S f (X)4573 840 w 10 R f (, which is)2 402 1 4638 840 t (stored compactly by rows:)3 1060 1 1570 960 t 10 S f (X)2680 960 w 7 R f (1 , 1)2 98 1 2756 980 t 10 R f (,)2862 960 w 10 S f (X)2912 960 w 7 R f (2 , 1)2 98 1 2988 980 t 10 R f (,)3094 960 w 10 S f (X)3144 960 w 7 R f (2 , 2)2 98 1 3220 980 t 10 R f (,)3326 960 w 10 S f (X)3376 960 w 7 R f (3 , 1)2 98 1 3452 980 t 10 R f (,)3558 960 w 10 S f (X)3608 960 w 7 R f (3 , 2)2 98 1 3684 980 t 10 R f (,)3790 960 w 10 S f (X)3840 960 w 7 R f (3 , 3)2 98 1 3916 980 t 10 R f (. . .)2 125 1 4055 935 t ( possible val-)2 533(. Other)1 302 2 4205 960 t (ues for IV\(COVMAT\) include:)3 1250 1 1570 1080 t (0 for no covariance matrix computation attempted;)6 2030 1 1845 1260 t (\2611 for an indefinite)3 825 1 1845 1380 t 10 I f (H)2714 1380 w 10 R f ([regard this as similar to singular convergence)6 1960 1 2830 1380 t (\(IV\(1\) = 7 \320 see \2473\)].)5 903 1 1820 1500 t (\2612 for too many)3 650 1 1845 1620 t 10 I f (x)2523 1620 w 10 R f ( com-)1 234(values rejected \(see \24711\) during finite-difference)5 1961 2 2595 1620 t (putation of)1 436 1 1820 1740 t 10 I f (H)2281 1740 w 10 R f (.)2353 1740 w 10 CW f (IV\(REGD\))890 1980 w 10 R f ( if positive, is the starting subscript in V for the regression diagnostic array)13 2991(\320 IV\(67\),)1 446 2 1420 1980 t 10 I f (RD)4882 1980 w 10 R f (.)5015 1980 w (IV\(REGD\))1570 2100 w 10 S f (\243)2038 2100 w 10 R f (0 means the same as IV\(COVMAT\) having this value.)8 2177 1 2118 2100 t 10 B f (CONFIDENCE INTERVALS)1 1281 1 970 2376 t 10 R f ( may wish to know confidence inter-)6 1464( You)1 222(for nonlinear least squares:)3 1078 3 2276 2376 t (vals for the components)3 960 1 720 2496 t 10 I f (x)1706 2496 w 7 I f (i)1761 2516 w 10 R f ( but explaining them requires)4 1171( have several options,)3 868( You)1 223(of the returned solution.)3 963 4 1815 2496 t ( you have)2 420( Suppose)1 405(some notation.)1 605 3 720 2616 t 10 I f (n)2191 2616 w 10 R f (observations and a model)3 1066 1 2282 2616 t 10 S f (f)3389 2616 w 10 R f (that attempts to explain them \320)5 1366 1 3482 2616 t 10 S f (f)4890 2616 w 10 R f (=)4984 2616 w (\()720 2736 w 10 S f (f)753 2736 w 7 R f (1)816 2756 w 10 R f (\()867 2736 w 10 I f (x)908 2736 w 10 R f (\),)960 2736 w 10 S f (f)1080 2736 w 7 R f (2)1143 2756 w 10 R f (\()1194 2736 w 10 I f (x)1235 2736 w 10 R f (\),)1287 2736 w (. . .)2 125 1 1432 2711 t (,)1582 2736 w 10 S f (f)1669 2736 w 7 I f (n)1732 2756 w 10 R f (\()1783 2736 w 10 I f (x)1824 2736 w 10 R f (\) \))1 74 1 1876 2736 t 7 I f (T)1961 2696 w 10 R f ( model parameters)2 809( decide to estimate the)4 1041(. You)1 284 3 2008 2736 t 10 I f (x)4203 2736 w 10 R f (by least squares:)2 732 1 4308 2736 t 10 I f (f)720 2906 w 10 R f (\()764 2906 w 10 I f (x)805 2906 w 10 R f (\) :)1 110 1 857 2906 t 10 S f (=)983 2906 w 7 R f (2)1112 2955 w (1)1112 2864 w 7 S1 f (_ __)1 71 1 1094 2885 t 7 I f (j)1206 3006 w 7 S f (=)1237 3006 w 7 R f (1)1287 3006 w 15 S f (S)1220 2936 w 7 I f (n)1247 2806 w 10 R f (\()1366 2906 w 10 S f (f)1407 2906 w 7 I f (j)1470 2926 w 10 R f (\()1506 2906 w 10 I f (x)1547 2906 w 10 R f (\))1599 2906 w 10 S f (-)1680 2906 w 10 I f (y)1775 2906 w 7 I f (j)1830 2926 w 10 R f (\))1866 2906 w 7 R f (2)1904 2866 w 10 R f ( diagonal entries of the covariance matrix computed with)8 2799(. The)1 294 2 1947 2906 t 10 S f (\357)720 3106 w 10 R f (IV\(COVREQ\))769 3106 w 10 S f (\357)1351 3106 w 10 R f ( \(i.e., standard deviations squared\) of the)6 1741(= 1 are estimates of the variances)6 1450 2 1445 3106 t 10 I f (x)4680 3106 w 7 I f (i)4735 3126 w 10 R f (. Two)1 277 1 4763 3106 t ( that the observations)3 870( \(1\))1 172(assumptions underlie these estimates:)3 1520 3 720 3226 t 10 I f (y)3313 3226 w 7 I f (j)3368 3246 w 10 R f ( whose)1 287(are subject to independent errors)4 1326 2 3427 3226 t (variances are well estimated by 1)5 1362 1 720 3356 t 13 I f (/)2114 3356 w 10 R f (\()2182 3356 w 10 I f (n)2223 3356 w 10 S f (-)2313 3356 w 10 I f (p)2408 3356 w 10 R f (\) times the residual sum of squares \(i.e., 2)8 1723 1 2466 3356 t (.)4197 3326 w 10 I f (f)4238 3356 w 10 R f (\()4282 3356 w 10 I f (x)4323 3356 w 7 I f (final)4378 3316 w 10 R f (\))4524 3356 w 13 I f (/)4597 3356 w 10 R f (\()4665 3356 w 10 I f (n)4706 3356 w 10 S f (-)4796 3356 w 10 I f (p)4891 3356 w 10 R f (\)\),)4949 3356 w (and \(2\) that approximating)3 1074 1 720 3476 t 10 I f (f)1822 3476 w 10 R f (by a second-order Taylor expansion does not introduce ``too much'' error into)11 3162 1 1878 3476 t ( apply to your prob-)4 807( first assumption is a standard one, but it may not)10 1999( The)1 208(the estimated covariance matrix.)3 1306 4 720 3596 t (lem \320 if you have a better estimate)7 1484 1 720 3716 t 10 S f (s)2237 3716 w 7 I f (better)2302 3735 w 7 R f (2)2302 3676 w 10 R f (for the variances of the)4 951 1 2507 3716 t 10 I f (y)3491 3716 w 7 I f (j)3546 3736 w 10 R f ( returned)1 366(, then you should scale the)5 1100 2 3574 3716 t (covariance matrix by)2 850 1 720 3846 t 7 R f (2)1624 3895 w (1)1624 3804 w 7 S1 f (_ __)1 71 1 1606 3825 t 10 R f (.)1716 3816 w 10 S f (s)1773 3846 w 7 I f (better)1838 3865 w 7 R f (2)1838 3806 w 10 R f (.)2042 3816 w (\()2099 3846 w 10 I f (n)2140 3846 w 10 S f (-)2230 3846 w 10 I f (p)2325 3846 w 10 R f (\))2383 3846 w 13 I f (/)2456 3846 w 10 R f ( V\(F\) = V\(10\) =)4 656(V\(F\), where)1 491 2 2524 3846 t 10 I f (f)3699 3846 w 10 R f (\()3743 3846 w 10 I f (x)3784 3846 w 7 I f (final)3839 3806 w 10 R f ( second assumption)2 789(\). The)1 266 2 3985 3846 t ( of the)2 267(generally founders when the variances)4 1554 2 720 3995 t 10 I f (y)2572 3995 w 7 I f (j)2627 4015 w 10 R f (are too large, where ``large'' depends on how nonlinear)8 2271 1 2686 3995 t 10 S f (f)4988 3995 w 10 R f ( techniques to compute a realistic covariance matrix and confi-)9 2544(is; you might have to resort to Monte-Carlo)7 1776 2 720 4115 t ( any rate, in posing the problem to the regression rou-)10 2204( At)1 156( do, see the end of \24717.\))6 995( you)1 180( \(If)1 154(dence intervals.)1 631 6 720 4235 t (tine, it is important that you scale the components of)9 2225 1 720 4355 t 10 S f (f)2984 4355 w 10 R f (and)3075 4355 w 10 I f (y)3258 4355 w 10 R f ( variances of the)3 695(\(correspondingly\) so the)2 1004 2 3341 4355 t (errors to which they are subject are all about the same.)10 2175 1 720 4475 t (The following code sets STDDEV\()4 1425 1 970 4631 t 10 I f (i)2395 4631 w 10 R f ( deviation of)2 515(\) to an estimate of the standard)6 1255 2 2423 4631 t 10 I f (x)4223 4631 w 7 I f (i)4278 4651 w 10 R f (in the case where)3 704 1 4336 4631 t (you know)1 397 1 720 4751 t 10 S f (s)1142 4751 w 7 I f (better)1207 4770 w 7 R f (2)1207 4711 w 10 R f (:)1379 4751 w 10 CW f (T = 0.5)2 420 1 1320 4931 t 10 S f (* s)1 134 1 1740 4931 t 7 I f (better)1879 4950 w 7 R f (2)1879 4891 w 10 S f (*)2075 4931 w 10 CW f (MAX0\(1,N-P\)/V\(F\))2125 4931 w (II = IV\(COVMAT\) \261 1)4 1140 1 1320 5051 t (DO 10 I = 1, P)5 840 1 1320 5171 t (II = II + I)4 660 1 1570 5291 t (STDDEV\(I\) = SQRT\(T)2 1080 1 1570 5411 t 10 S f (*)2650 5411 w 10 CW f (V\(II\)\))2700 5411 w (10 CONTINUE)1 1020 1 1030 5531 t 10 R f (If assumption \(1\) is valid, omit the first line as well as ``)12 2251 1 720 5711 t 10 CW f (T)2971 5711 w 10 S f (*)3031 5711 w 10 R f ('' in the penultimate line.)4 1013 1 3081 5711 t (After making further assumptions about the errors, you can relate STDDEV\()10 3113 1 970 5867 t 10 I f (i)4083 5867 w 10 R f ( inter-)1 247(\) to a confidence)3 682 2 4111 5867 t (val for)1 281 1 720 5987 t 10 I f (x)1044 5987 w 7 I f (i)1099 6007 w 10 R f ( example, if the errors in the)6 1236(. For)1 232 2 1127 5987 t 10 I f (y)2637 5987 w 7 I f (j)2692 6007 w 10 R f (are normally distributed with zero mean, then [)7 1999 1 2762 5987 t 10 I f (x)4761 5987 w 7 I f (i)4810 6006 w (final)4810 5947 w 10 R f (\261)4990 5987 w (1. 96)1 183 1 720 6107 t (.)911 6077 w (STDDEV\()936 6107 w 10 I f (i)1363 6107 w 10 R f (\),)1391 6107 w 10 I f (x)1477 6107 w 7 I f (i)1526 6126 w (final)1526 6067 w 10 R f ( 96)1 108(+ 1.)1 159 2 1692 6107 t (.)1967 6077 w (STDDEV\()1992 6107 w 10 I f (i)2419 6107 w 10 R f (\)] is a 95% confidence interval for)6 1392 1 2447 6107 t 10 I f (x)3868 6107 w 7 I f (i)3923 6127 w 10 R f ( 1.96 to 1.645 to)4 672(. \(Change)1 417 2 3951 6107 t (get a 90% confidence interval and to 2.576 to get a 99% confidence interval.\))13 3090 1 720 6227 t 10 B f ( \(or rejecting\))2 586(11. Identifying)1 648 2 720 6467 t 10 BI f (x)1979 6467 w 10 R f (When you compute)2 822 1 970 6623 t 10 S f (\321)1837 6623 w 10 I f (f)1924 6623 w 10 R f (\()1968 6623 w 10 I f (x)2009 6623 w 10 R f ( are also)2 374(\) analytically, you must often use intermediate quantities that)8 2605 2 2061 6623 t (needed for computing)2 914 1 720 6743 t 10 I f (f)1678 6743 w 10 R f (\()1722 6743 w 10 I f (x)1763 6743 w 10 R f ( find it convenient to save such quantities for use in computing)11 2710( may)1 216(\). You)1 299 3 1815 6743 t 10 S f (\321)720 6863 w 10 I f (f)807 6863 w 10 R f (\()851 6863 w 10 I f (x)892 6863 w 10 R f ( may first ask for)4 746( optimization routine)2 869( the)1 187( there is a complication:)4 1020(\). But)1 268 5 944 6863 t 10 I f (f)4075 6863 w 10 R f (\()4119 6863 w 10 I f (x)4160 6863 w 7 I f (a)4215 6823 w 10 R f (\), then)1 271 1 4266 6863 t 10 I f (f)4578 6863 w 10 R f (\()4622 6863 w 10 I f (x)4663 6863 w 7 I f (b)4718 6823 w 10 R f (\), then)1 271 1 4769 6863 t 10 S f (\321)720 6983 w 10 I f (f)807 6983 w 10 R f (\()851 6983 w 10 I f (x)892 6983 w 7 I f (a)947 6943 w 10 R f (\), i.e., the)2 387 1 998 6983 t 10 I f (x)1415 6983 w 10 R f (at which)1 346 1 1489 6983 t 10 S f (\321)1865 6983 w 10 I f (f)1952 6983 w 10 R f ( which)1 273(is evaluated may not be the one at)7 1391 2 2010 6983 t 10 I f (f)3703 6983 w 10 R f ( It)1 115(was most recently evaluated.)3 1165 2 3760 6983 t (usually suffices to save two sets of intermediate quantities, corresponding to the two)12 3371 1 720 7103 t 10 I f (x)4116 7103 w 10 R f (values at which)2 621 1 4185 7103 t 10 I f (f)4831 7103 w 10 R f (was)4885 7103 w ( the invocation count for)4 1054( can use)2 359( You)1 241(most recently evaluated.)2 1011 4 720 7223 t 10 I f (f)3428 7223 w 10 R f (to identify these sets of intermediate)5 1541 1 3499 7223 t ( 16, 1990)2 375( October)1 1677( 14 -)2 183(Optimization -)1 2085 4 720 7680 t cleartomark showpage saveobj restore end %%PageBoundingBox: 61 8 514 764 %%EndPage: 14 15 %%Page: 15 16 %%PageBoundingBox: (atend) DpostDict begin /saveobj save def mark 16 pagesetup 8 R f (PORT)720 480 w 10 R f ( Usage Summary)2 688(library Optimization)1 3406 2 946 480 t ( you supply, say, sub-)4 908( you use a forward-communication optimization routine, one to which)9 2874(quantities. If)1 538 3 720 840 t (routines CALCF and CALCG for computing)5 1837 1 720 960 t 10 I f (f)2590 960 w 10 R f (\()2634 960 w 10 I f (x)2675 960 w 10 R f (\) and)1 210 1 2727 960 t 10 S f (\321)2970 960 w 10 I f (f)3057 960 w 10 R f (\()3101 960 w 10 I f (x)3142 960 w 10 R f (\), then the calling sequence for these subrou-)7 1846 1 3194 960 t ( to identify)2 459(tines includes an integer parameter NF that you can use)9 2296 2 720 1080 t 10 I f (x)3510 1080 w 10 R f ( CALCF, NF is the invocation)5 1262(. For)1 224 2 3554 1080 t ( value that was)3 596(count for CALCF \(i.e., the number of times CALCF has been called\); for CALCG, NF is the)16 3724 2 720 1200 t (supplied to CALCF when CALCF was called with the)8 2188 1 720 1320 t 10 I f (x)2936 1320 w 10 R f ( you are calling a)4 699( If)1 119(now being passed to CALCG.)4 1214 3 3008 1320 t ( that would be passed to CALCF is in)8 1826(reverse-communication routine \(\2471c\), then the NF value)6 2494 2 720 1440 t ( \(Do)1 207( in IV\(NFGCAL\) = IV\(7\).)4 1059(IV\(NFCALL\) = IV\(6\), and the NF value that would be passed to CALCG is)13 3054 3 720 1560 t ( should not change NF unless)5 1185(not change IV\(NFCALL\) or IV\(NFGCAL\); subroutines CALCF and CALCG)8 3135 2 720 1680 t (they wish to reject)3 735 1 720 1800 t 10 I f (x)1480 1800 w 10 R f (, as described in the next paragraph.\))6 1468 1 1524 1800 t 10 B f (Rejecting)970 1956 w 10 BI f (x)1416 1956 w 10 R f ( step or will otherwise)4 960( the optimization routine will attempt too large a)8 2074(: Sometimes)1 540 3 1466 1956 t (request that)1 479 1 720 2076 t 10 I f (f)1240 2076 w 10 R f ( routine to back off and try a)7 1244( can tell the)3 511( You)1 238(be evaluated outside its effective domain.)5 1738 4 1309 2076 t ( pass CALCF\),)2 627( you are using a forward-communication routine \(to which you)9 2614( if)1 122(shorter step as follows:)3 957 4 720 2196 t ( NF to 0 and return; if you are calling a reverse-communication routine, set)13 3364(then have CALCF set)3 956 2 720 2316 t ( can also reject)3 625( \(CALCG)1 431(IV\(TOOBIG\) = IV\(2\) to 1.)4 1114 3 720 2436 t 10 I f (x)2925 2436 w 10 R f (by setting NF to 0, or you can reject)8 1520 1 3004 2436 t 10 I f (x)4559 2436 w 10 R f (by setting)1 402 1 4638 2436 t ( iteration driver asks you to compute)6 1471(IV\(TOOBIG\) to 1 when a reverse-communication)5 2013 2 720 2556 t 10 S f (\321)4230 2556 w 10 I f (f)4317 2556 w 10 R f (\()4361 2556 w 10 I f (x)4402 2556 w 10 R f (\), but then you)3 586 1 4454 2556 t ( encounter an)2 547( routines assume something serious is wrong if they)8 2103( the)1 176(will get an error return:)4 947 4 720 2676 t 10 I f (x)4523 2676 w 10 R f (where)4597 2676 w 10 I f (f)4870 2676 w 10 R f (\()4914 2676 w 10 I f (x)4955 2676 w 10 R f (\))5007 2676 w (can be evaluated but)3 817 1 720 2796 t 10 S f (\321)1562 2796 w 10 I f (f)1649 2796 w 10 R f (\()1693 2796 w 10 I f (x)1734 2796 w 10 R f (\) cannot.\))1 382 1 1786 2796 t 10 B f (12. STOPX)1 509 1 720 3036 t 10 R f ( an interactive environment, then you can arrange for)8 2199(If you use the PORT optimization routines in)7 1871 2 970 3192 t ( of)1 110(them to respond to the ``BREAK'' key \320 to check before each evaluation)12 3007 2 720 3312 t 10 I f (f)3864 3312 w 10 R f (\()3908 3312 w 10 I f (x)3949 3312 w 10 R f (\) whether ``BREAK'' has)3 1039 1 4001 3312 t ( do this, you must supply a logical)7 1422( To)1 168( if so.)2 239(been pressed and to return in a way that allows restarts \(\24713\))11 2491 4 720 3432 t ( that returns .TRUE. exactly when ``BREAK'' has been pressed since the last time STOPX)14 3644(function STOPX)1 676 2 720 3552 t ( other than Fortran\) should behave as)6 1516( STOPX \(which will likely be written in a language)9 2098( Your)1 259(was called.)1 447 4 720 3672 t (though it began)2 622 1 720 3792 t 10 CW f (LOGICAL FUNCTION STOPX\(DUMMY\))2 1740 1 1070 3972 t (INTEGER DUMMY)1 780 1 1070 4092 t 10 R f ( When)1 306( by the syntax of Fortran 66\).)6 1276(STOPX should ignore its parameter DUMMY \(which is required)8 2738 3 720 4272 t (STOPX returns .TRUE., you get a return with IV\(1\) = 11.)10 2314 1 720 4392 t 10 B f (13. Restarting)1 624 1 720 4632 t 10 R f (If you get a return with IV\(1\))6 1223 1 970 4788 t 10 S f (<)2228 4788 w 10 R f (12 \(from either a forward- or reverse-communication optimization)7 2722 1 2318 4788 t ( invoke the routine)3 782( Just)1 216( the algorithm where it left off.)6 1294(routine \320 see \2471c and \2473\), then you can resume)9 2028 4 720 4908 t ( can)1 174( You)1 233( for the return you got.)5 959(again, usually after changing the IV or V input components responsible)10 2954 4 720 5028 t (even write the IV and V arrays,)6 1260 1 720 5148 t 10 I f (x)2006 5148 w 10 R f ( storage device, read)3 819(, and other parameters \(as appropriate\) on an auxiliary)8 2171 2 2050 5148 t ( is sometimes useful for)4 1007( This)1 241( resume the algorithm.)3 938(them in later \(perhaps in another session\), and then)8 2134 4 720 5268 t (checkpointing or debugging.)2 1146 1 720 5388 t 10 B f ( IV components)2 672(14. Output)1 487 2 720 5628 t 10 R f ( describes IV components \(listed alphabetically\) that are given)8 2527( It)1 115( skip this section.)3 707(You can probably)2 721 4 970 5784 t (values by the relevant PORT optimization routines.)6 2057 1 720 5904 t 10 CW f (IV\(A\))1070 6144 w 10 R f ( permutation)1 509( [general linear constraints only] is the starting subscript in IV for a)12 2690(\320 IV\(98\))1 421 3 1420 6144 t (array,)1570 6264 w 10 I f (a)1827 6264 w 10 S f (=)1926 6264 w 10 R f (\()2030 6264 w 10 I f (a)2071 6264 w 7 R f (1)2132 6284 w 10 R f (,)2183 6264 w 10 I f (a)2249 6264 w 7 R f (2)2310 6284 w 10 R f (,)2361 6264 w (. . .)2 125 1 2452 6239 t (,)2610 6264 w 10 I f (a)2676 6264 w 7 I f (m)2737 6284 w 7 S f (+)2803 6284 w 7 I f (p)2853 6284 w 10 R f (\), where)1 329 1 2904 6264 t 10 I f (m)3260 6264 w 10 R f (is the number of general constraints \(1.2\).)6 1681 1 3359 6264 t ( below\),)1 336(Together with IV\(ME\), IV\(ME1\), IV\(MC\), and IV\(PC\) \(all described)8 2849 2 1570 6384 t 10 I f (a)4789 6384 w 10 R f (tells)4873 6384 w ( various constraints at)3 892(how the algorithm regards the)4 1226 2 1570 6504 t 10 I f (x)3719 6504 w 7 I f (final)3774 6464 w 10 R f (, the returned)2 541 1 3912 6504 t 10 I f (x)4484 6504 w 10 R f ( 1)1 81(: for)1 200 2 4528 6504 t 10 S f (\243)4840 6504 w 10 I f (i)4926 6504 w 10 S f (\243)4985 6504 w 10 R f (IV\(ME1\), constraint)1 824 1 1570 6624 t 10 I f (a)2428 6624 w 7 I f (i)2489 6644 w 10 R f ( \(see IV\(SOLPRT\) in \2476a\);)4 1127(is a redundant equality constraint)4 1362 2 2551 6624 t (for IV\(ME1\))1 513 1 1570 6744 t 10 S f (<)2109 6744 w 10 I f (i)2190 6744 w 10 S f (\243)2244 6744 w 10 R f (IV\(ME1\) + IV\(ME\), constraint)3 1245 1 2325 6744 t 10 I f (a)3596 6744 w 7 I f (i)3657 6764 w 10 R f (is a \(nonredundant\) equality con-)4 1329 1 3711 6744 t (straint; and for IV\(ME1\) + IV\(ME\))5 1421 1 1570 6864 t 10 S f (<)3018 6864 w 10 I f (i)3100 6864 w 10 S f (\243)3155 6864 w 10 R f ( constraint)1 422(IV\(ME1\) + IV\(ME\) + IV\(MC\),)4 1264 2 3237 6864 t 10 I f (a)4951 6864 w 7 I f (i)5012 6884 w 10 R f ( IV\(MC\) + IV\(PC\))3 758( \(If)1 151(is an active inequality constraint.)4 1326 3 1570 6984 t 10 S f (>)3832 6984 w 10 I f (p)3914 6984 w 10 R f ( last)1 165(, then the)2 373 2 3964 6984 t 10 I f (p)4528 6984 w 10 R f (\261 [IV\(MC\))1 436 1 4604 6984 t (+ IV\(PC\)] such inequality constraints are redundant at)7 2166 1 1570 7104 t 10 I f (x)3761 7104 w 7 I f (final)3816 7064 w 10 R f (.\))3954 7104 w (The numbering within)2 908 1 1695 7284 t 10 I f (a)2635 7284 w 10 R f ( that)1 183( Routines)1 414(of the constraints deserves an explanation.)5 1726 3 2717 7284 t ( Optimization)1 2052( 15 -)2 183( -)1 1389(October 16, 1990)2 696 4 720 7680 t cleartomark showpage saveobj restore end %%PageBoundingBox: 61 8 514 764 %%EndPage: 15 16 %%Page: 16 17 %%PageBoundingBox: (atend) DpostDict begin /saveobj save def mark 17 pagesetup 10 R f (Optimization Usage Summary)2 1216 1 720 480 t 8 R f (PORT)4548 480 w 10 R f (library)4774 480 w (handle general linear constraints allow both simple bounds \(1.1\) and general linear)11 3470 1 1570 840 t ( 1)1 79( for)1 170( constraints are numbered as follows:)5 1509( The)1 209(constraints \(1.2\).)1 678 5 1570 960 t 10 S f (\243)4256 960 w 10 I f (i)4352 960 w 10 S f (\243)4421 960 w 10 I f (p)4517 960 w 10 R f ( simple)1 297(, the)1 176 2 4567 960 t (lower-bound constraint)1 948 1 1570 1080 t 10 I f (b)2562 1080 w 10 S f (_)2560 1080 w 7 I f (i)2617 1099 w (x)2617 1040 w 10 S f (\243)2697 1080 w 10 I f (x)2793 1080 w 7 I f (i)2848 1100 w 10 R f (has index)1 398 1 2919 1080 t 10 I f (i)3360 1080 w 10 R f (and the simple upper-bound constraint)4 1609 1 3431 1080 t 10 I f (x)1570 1206 w 7 I f (i)1625 1226 w 10 S f (\243)1694 1206 w 10 I f (b)1790 1206 w 10 S1 f (_)1795 1113 w 7 I f (i)1845 1225 w (x)1845 1138 w 10 R f (has index)1 442 1 1971 1206 t 10 S f (-)2501 1206 w 10 I f (i)2572 1206 w 10 R f (; for 1)2 370 1 2600 1206 t 10 S f (\243)3011 1206 w 10 I f (i)3107 1206 w 10 S f (\243)3176 1206 w 10 I f (m)3272 1206 w 10 R f (, the general lower-bound constraint)4 1696 1 3344 1206 t 10 I f (b)1570 1376 w 10 S f (_)1568 1376 w 7 I f (i)1625 1395 w (c)1625 1336 w 10 S f (\243)1705 1376 w 7 I f (j)1803 1476 w 7 S f (=)1834 1476 w 7 R f (0)1884 1476 w 15 S f (S)1817 1406 w 7 I f (p)1844 1276 w 10 I f (C)1963 1376 w 7 I f (i j)1 45 1 2041 1396 t 10 I f (x)2102 1376 w 7 I f (j)2157 1396 w 10 R f (has index)1 456 1 2286 1376 t 10 I f (i)2843 1376 w 10 S f (+)2920 1376 w 10 I f (p)3024 1376 w 10 R f ( upper-bound constraint)2 1104(and the general)2 761 2 3175 1376 t 7 I f (j)1572 1726 w 7 S f (=)1603 1726 w 7 R f (0)1653 1726 w 15 S f (S)1586 1656 w 7 I f (p)1613 1526 w 10 I f (C)1732 1626 w 7 I f (i j)1 45 1 1810 1646 t 10 I f (x)1871 1626 w 7 I f (j)1926 1646 w 10 S f (\243)1995 1626 w 10 I f (b)2091 1626 w 10 S1 f (_)2096 1533 w 7 I f (i)2146 1645 w (c)2146 1558 w 10 R f (has index)1 380 1 2210 1626 t 10 S f (-)2615 1626 w 10 R f (\()2686 1626 w 10 I f (i)2727 1626 w 10 S f (+)2804 1626 w 10 I f (p)2908 1626 w 10 R f (\).)2966 1626 w 10 CW f (IV\(AI\))1010 1891 w 10 R f ( [general linear constraints only] is the starting subscript in IV for an array)13 3008(\320 IV\(91\))1 421 2 1420 1891 t 10 I f (a)4878 1891 w 11 R f (\304)4887 1886 w 10 R f (of)4957 1891 w ( multipliers corresponding to)3 1182(indices of the Lagrange)3 966 2 1570 2011 t 10 I f (x)3751 2011 w 7 I f (final)3806 1971 w 10 R f ( entries in this array)4 825(. \(The)1 271 2 3944 2011 t (also appear in the)3 710 1 1570 2131 t 10 I f (a)2308 2131 w 10 R f ( \320 here)2 329(array described above with IV\(A\), but in a different order)9 2325 2 2386 2131 t ( more on the multipliers themselves, see)6 1649( For)1 196(they are sorted on their absolute values.)6 1625 3 1570 2251 t ( are)1 146( There)1 282(IV\(AM\) below.\))1 659 3 1570 2371 t 10 I f (p)2682 2371 w 10 R f (\261 IV\(PC\) such multipliers \(see IV\(PC\) below\).)6 1867 1 2757 2371 t 10 CW f (IV\(AM\))1010 2551 w 10 R f ( constraints only] is the starting subscript in V for the Lagrange)11 2588( [general linear)2 611(\320 IV\(95\))1 421 3 1420 2551 t (multiplier array)1 629 1 1570 2671 t 10 S f (l)2229 2671 w 10 R f ( \2476a\) controls the)3 708( \(see)1 190( IV\(SOLPRT\))1 599(mentioned with IV\(AI\) above.)3 1229 4 2314 2671 t ( multipliers)1 472( The)1 218(printing of this array.)3 888 3 1570 2791 t 10 S f (l)3186 2791 w 7 I f (i)3252 2811 w 10 R f (are such that if)3 629 1 3318 2791 t 10 I f (C)3985 2791 w 10 R f ( expanded to)2 538(in \(1.2\) is)2 412 2 4090 2791 t (include \(1.1\) in the first)4 946 1 1570 2911 t 10 I f (p)2541 2911 w 10 R f (rows and)1 363 1 2616 2911 t 10 I f (C)3004 2911 w 7 I f (i)3082 2931 w 10 R f (denotes the)1 452 1 3135 2911 t 10 I f (i)3612 2911 w 10 R f (th row of this expanded)4 943 1 3640 2911 t 10 I f (C)4608 2911 w 10 R f (, then)1 222 1 4675 2911 t 7 I f (i)2574 3241 w 7 S f (=)2610 3241 w 7 R f (1)2660 3241 w 15 S f (S)2590 3171 w 7 I f (p)2481 3041 w 7 S f (-)2532 3041 w 7 R f (IV\(PC\))2582 3041 w 10 S f (l)2828 3141 w 7 I f (i)2894 3161 w 10 R f (sign \()1 208 1 2954 3141 t 10 I f (a)3170 3141 w 11 R f (\304)3179 3136 w 7 I f (i)3231 3161 w 10 R f (\))3267 3141 w 10 I f (C)3340 3141 w 7 S f (\357)3418 3172 w 7 I f (a)3451 3161 w 8 R f (\304)3458 3158 w 4 I f (i)3492 3175 w 7 S f (\357)3508 3172 w 10 S f (= \321)1 175 1 3576 3141 t 10 I f (f)3767 3141 w 10 R f (\()3811 3141 w 10 I f (x)3852 3141 w 7 I f (final)3907 3101 w 10 R f (\) ,)1 74 1 4053 3141 t (where)1570 3406 w 10 I f (a)1838 3406 w 11 R f (\304)1847 3401 w 10 R f (is the index array described with IV\(AI\) above.)7 1889 1 1913 3406 t 10 CW f (IV\(COVMAT\))770 3586 w 10 R f ( \24710.)1 200(\320 see)1 277 2 1420 3586 t 10 CW f (IV\(D\))1070 3766 w 10 R f ( is the starting subscript in V for the scale vector)10 2036( [regression routines only])3 1078(\320 IV\(27\))1 421 3 1420 3766 t 10 I f (d)4990 3766 w 10 R f (\(\2474\).)1570 3886 w 10 CW f (IV\(G\))1070 4066 w 10 R f ( the starting sub-)3 696( [except for some reverse-communication iteration drivers] is)7 2503(\320 IV\(28\))1 421 3 1420 4066 t (script in V for the gradient vector)6 1336 1 1570 4186 t 10 S f (\321)2931 4186 w 10 I f (f)3018 4186 w 10 R f (\()3062 4186 w 10 I f (x)3103 4186 w 7 I f (final)3158 4146 w 10 R f (\).)3304 4186 w 10 CW f (IV\(LASTIV\))770 4366 w 10 R f ( is the minimum acceptable value for LIV, the length of the IV array.)13 2758(\320 IV\(44\))1 421 2 1420 4366 t 10 CW f (IV\(LASTV\))830 4546 w 10 R f ( is the minimum acceptable value for LV, the length of the V array.)13 2692(\320 IV\(45\))1 421 2 1420 4546 t 10 CW f (IV\(MC\))1010 4726 w 10 R f ( number of inequality constraints \(1.1\) or)6 1657( [general linear constraints only] is the)6 1542(\320 IV\(83\))1 421 3 1420 4726 t (\(1.2\) active at)2 567 1 1570 4846 t 10 I f (x)2170 4846 w 7 I f (final)2225 4806 w 10 R f ( below)1 276(, excluding equality constraints \(see IV\(ME\) and IV\(ME1\))7 2401 2 2363 4846 t (and IV\(A\) above\).)2 733 1 1570 4966 t 10 CW f (IV\(ME\))1010 5146 w 10 R f ( nonredundant equality con-)3 1153( [general linear constraints only] is the number of)8 2046(\320 IV\(86\))1 421 3 1420 5146 t ( constraints)1 487(straints \320 linearly independent)3 1347 2 1570 5316 t 10 I f (b)3458 5316 w 10 S f (_)3456 5316 w 7 I f (i)3513 5335 w (x)3513 5276 w 10 S f (\243)3593 5316 w 10 I f (x)3689 5316 w 7 I f (i)3744 5336 w 10 S f (\243)3813 5316 w 10 I f (b)3909 5316 w 10 S1 f (_)3914 5223 w 7 I f (i)3964 5335 w (x)3964 5248 w 10 R f (or)4057 5316 w 10 I f (b)4194 5316 w 10 S f (_)4192 5316 w 7 I f (i)4249 5335 w (c)4249 5276 w 10 S f (\243)4329 5316 w 7 I f (j)4427 5416 w 7 S f (=)4458 5416 w 7 R f (0)4508 5416 w 15 S f (S)4441 5346 w 7 I f (p)4468 5216 w 10 I f (C)4587 5316 w 7 I f (i j)1 45 1 4665 5336 t 10 I f (x)4726 5316 w 7 I f (j)4781 5336 w 10 S f (\243)4850 5316 w 10 I f (b)4946 5316 w 10 S1 f (_)4951 5223 w 7 I f (i)5001 5335 w (c)5001 5248 w 10 R f (from \(1.1\) and \(1.2\) having)4 1092 1 1570 5522 t 10 I f (b)2687 5522 w 10 S f (_)2685 5522 w 7 I f (i)2742 5541 w (x)2742 5482 w 10 S f (=)2830 5522 w 10 I f (b)2934 5522 w 10 S1 f (_)2939 5429 w 7 I f (i)2989 5541 w (x)2989 5454 w 10 R f (or)3053 5522 w 10 I f (b)3161 5522 w 10 S f (_)3159 5522 w 7 I f (i)3216 5541 w (c)3216 5482 w 10 S f (=)3304 5522 w 10 I f (b)3408 5522 w 10 S1 f (_)3413 5429 w 7 I f (i)3463 5541 w (c)3463 5454 w 10 R f ( also IV\(A\) above.)3 742(. See)1 219 2 3502 5522 t 10 CW f (IV\(ME1\))950 5702 w 10 R f ( only] is the number of equality constraints being)8 2093( [general linear constraints)3 1106(\320 IV\(87\))1 421 3 1420 5702 t ( the nonredundant equality constraints)4 1550(ignored because they are linearly dependent on)6 1920 2 1570 5822 t ( constraints is thus IV\(ME\) +)5 1289( total number of equality)4 1080( The)1 228(\(see IV\(ME\) above\).)2 873 4 1570 5942 t ( also IV\(A\) above.)3 742(IV\(ME1\). See)1 590 2 1570 6062 t 10 CW f (IV\(NEXTIV\))770 6242 w 10 R f ( most routines it should)4 964( For)1 195( of the next free component in IV.)7 1400( is the subscript)3 640(\320 IV\(46\))1 421 5 1420 6242 t ( give it a smaller value \(if they)7 1314(have the value IV\(LASTIV\) + 1, but some routines)8 2156 2 1570 6362 t (release scratch space used only when they start up\).)8 2058 1 1570 6482 t 10 CW f (IV\(NEXTV\))830 6662 w 10 R f ( to)1 152( Analogously)1 610( of the next free component in V.)7 1668( is the subscript)3 769(\320 IV\(47\))1 421 5 1420 6662 t (IV\(NEXTIV\), it usually has the value IV\(LASTV\) + 1.)8 2207 1 1570 6782 t 10 CW f (IV\(NFCALL\))770 6962 w 10 R f ( evaluations \(evaluations of)3 1107( is the number of function)5 1040(\320 IV\(6\))1 371 3 1420 6962 t 10 I f (f)3965 6962 w 10 R f (\()4009 6962 w 10 I f (x)4050 6962 w 10 R f (\)\) performed, including)2 938 1 4102 6962 t (evaluations for computing a covariance matrix or regression diagnostics but excluding)10 3470 1 1570 7082 t ( derivative approximations \(see)3 1373(extra evaluations for computing finite-difference)4 2097 2 1570 7202 t ( 16, 1990)2 375( October)1 1677( 16 -)2 183(Optimization -)1 2085 4 720 7680 t cleartomark showpage saveobj restore end %%PageBoundingBox: 61 8 514 764 %%EndPage: 16 17 %%Page: 17 18 %%PageBoundingBox: (atend) DpostDict begin /saveobj save def mark 18 pagesetup 8 R f (PORT)720 480 w 10 R f ( Usage Summary)2 688(library Optimization)1 3406 2 946 480 t (IV\(NGCALL\) below\).)1 903 1 1570 840 t 10 CW f (IV\(NFCOV\))830 1020 w 10 R f ( is the number of function evaluations performed just for)9 2455( [regression only])2 744(\320 IV\(52\))1 421 3 1420 1020 t ( matrix or regression diagnostics, excluding extra evaluations)7 2501(computing a covariance)2 969 2 1570 1140 t ( \(see IV\(NGCALL\) below\).)3 1134(for computing finite-difference derivative approximations)4 2336 2 1570 1260 t (The number of function evaluations reported in the summary statistics controlled by)11 3470 1 1570 1380 t (IV\(STATPR\) \(see \2476a\) is IV\(NFCALL\) \261 IV\(NFCOV\).)6 2243 1 1570 1500 t 10 CW f (IV\(NGCALL\))770 1680 w 10 R f ( performed \(when you provide)4 1227( is either the total number of gradient evaluations)8 1972(\320 IV\(30\))1 421 3 1420 1680 t ( or the number of additional function evaluations required to com-)10 2656(analytic derivatives\))1 814 2 1570 1800 t ( the latter case, the total number of)7 1393( In)1 134(pute finite-difference derivative approximations.)3 1943 3 1570 1920 t (function evaluations is thus IV\(NFCALL\) + IV\(NGCALL\).)6 2389 1 1570 2040 t 10 CW f (IV\(NGCOV\))830 2220 w 10 R f ( gradient evaluations performed just for computing)6 2072( is the number of additional)5 1127(\320 IV\(53\))1 421 3 1420 2220 t ( number of gradient evaluations)4 1334( The)1 222(a covariance matrix or regression diagnostics.)5 1914 3 1570 2340 t ( summary statistics controlled by IV\(STATPR\) \(see \2476a\) is)8 2786(reported in the)2 684 2 1570 2460 t (IV\(NGCALL\) \261 IV\(NGCOV\).)2 1227 1 1570 2580 t 10 CW f (IV\(NITER\))830 2760 w 10 R f ( number of gradient evaluations)4 1338( The)1 222( number of iterations performed.)4 1368( is the)2 271(\320 IV\(31\))1 421 5 1420 2760 t ( regression diagnostic computations\) is usually)5 1884(\(aside from those used in covariance or)6 1586 2 1570 2880 t ( IV\(NITER\), depending whether or not the final iteration produced)9 2726(IV\(NITER\) + 1 or)3 744 2 1570 3000 t (an acceptable new iterate.)3 1029 1 1570 3120 t 10 CW f (IV\(PC\))1010 3300 w 10 R f ( dimension of the free variable space at)7 1621( [general linear constraints only] is the)6 1578(\320 IV\(90\))1 421 3 1420 3300 t 10 I f (x)1570 3420 w 7 I f (final)1625 3380 w 10 R f (; see IV\(A\) above.)3 736 1 1763 3420 t 10 CW f (IV\(SUSED\))830 3600 w 10 R f ( the sequence of models for)5 1130( [regression only] describes)3 1115(\320 IV\(64\))1 421 3 1420 3600 t 10 I f (f)4117 3600 w 10 R f (considered in the last)3 864 1 4176 3600 t ( in the MODEL column)4 991(iteration \(see [1]\); IV\(SUSED\) determines what gets printed)7 2479 2 1570 3720 t ( means ``G'', 2 means ``S'', 3 means ``G\261S'' \(i.e.,)9 2085( 1)1 107(of the iteration summary \(\2476b\):)4 1278 3 1570 3840 t ( ``S'' model\), 4 means)4 937(the algorithm first tried the ``G'' model, then switched to the)10 2533 2 1570 3960 t (``S\261G'', 5 means ``G\261S\261G'' \(i.e., the algorithm first tried the ``G'' model, then the)13 3470 1 1570 4080 t (``S'' model, then returned to the ``G'' model\), and 6 means ``S\261G\261S''.)11 2844 1 1570 4200 t 10 B f ( V components)2 633(15. Output)1 487 2 720 4440 t 10 R f ( describes \(alphabetically\) V components to which)6 2048( It)1 115( section most people can ignore.)5 1307(This is another)2 600 4 970 4596 t (various PORT optimization routines supply values.)5 2050 1 720 4716 t 10 CW f (V\(DGNORM\))830 4956 w 10 R f ( =)1 81(\320 V\(1\))1 338 2 1420 4956 t 10 S f (\357 \357)1 73 1 1864 4973 t 10 I f (D)1936 4956 w 7 S f (-)2019 4916 w 7 R f (1)2069 4916 w 10 S f (\321)2120 4956 w 10 I f (f)2207 4956 w 10 R f (\()2251 4956 w 10 I f (x)2292 4956 w 7 I f (final)2347 4916 w 10 R f (\))2493 4956 w 10 S f (\357 \357)1 73 1 2526 4973 t 10 R f (, where)1 293 1 2566 4956 t 10 I f (D)2884 4956 w 10 R f (is given by \(4.1\).)3 680 1 2981 4956 t 10 CW f (V\(DSTNRM\))830 5136 w 10 R f ( =)1 91(\320 V\(2\))1 338 2 1420 5136 t 10 S f (\357 \357)1 73 1 1884 5153 t 10 I f (D)1956 5136 w 10 R f (\()2036 5136 w 10 I f (x)2077 5136 w 10 S f (-)2161 5136 w 10 I f (x)2256 5136 w 7 I f (prev)2311 5096 w 10 R f (\))2451 5136 w 10 S f (\357 \357)1 73 1 2484 5153 t 10 R f ( last step taken \(or, if the)6 1056(, the scaled Euclidean length of the)6 1460 2 2524 5136 t (final iteration did not change)4 1154 1 1570 5256 t 10 I f (x)2749 5256 w 10 R f (, of the last step attempted\).)5 1107 1 2793 5256 t 10 CW f (V\(F\))1130 5436 w 10 R f ( current function value,)3 955( is the)2 253(\320 V\(10\))1 388 3 1420 5436 t 10 I f (f)3049 5436 w 10 R f (\()3093 5436 w 10 I f (x)3134 5436 w 7 I f (final)3189 5396 w 10 R f ( nonlinear least squares, this is)5 1261(\). For)1 255 2 3335 5436 t 10 I f (half)4884 5436 w 10 R f (the current residual sum of squares.)5 1419 1 1570 5556 t 10 CW f (V\(F0\))1070 5736 w 10 R f ( is the function value of)5 946(\320 V\(13\))1 388 2 1420 5736 t 10 I f (f)2779 5736 w 10 R f (\()2823 5736 w 10 I f (x)2864 5736 w 10 R f (\) at the start of the last iteration.)7 1276 1 2916 5736 t 10 CW f (V\(NREDUC\))830 5916 w 10 R f ( the maximum reduction in)4 1123( if positive \(or zero with V\(STPPAR\) = 0\), is)9 1886(\320 V\(6\),)1 363 3 1420 5916 t 10 I f (f)4827 5916 w 10 R f (that)4890 5916 w ( = 0 with V\(STPPAR\))4 926( V\(NREDUC\))1 609(the algorithm thinks is yet possible.)5 1473 3 1570 6036 t 10 S f (>)4612 6036 w 10 R f (0 means)1 339 1 4701 6036 t ( constraints, projected Hessian \320 projected)5 1781(the current Hessian \(or, for general linear)6 1689 2 1570 6156 t ( V\(NREDUC\))1 601( If)1 143(onto the free-variable space\) is not positive definite.)7 2268 3 1570 6276 t 10 S f (<)4634 6276 w 10 R f (0, then)1 299 1 4741 6276 t 10 S f (-)1570 6406 w 10 R f (V\(PREDUC\))1641 6406 w 13 I f (/)2206 6406 w 10 R f ( compared in the)3 704(V\(F0\) is the quantity against which V\(SCTOL\) is)7 2062 2 2274 6406 t ( described in \2476b is)4 853( quantity NPRELDF)2 863( The)1 225(singular-convergence test \320 see \2475.)4 1529 4 1570 6526 t (V\(NREDUC\))1570 6656 w 13 I f (/)2151 6656 w 10 R f (max{V\(F\), V\(F0\)}.)1 781 1 2219 6656 t 10 CW f (V\(PREDUC\))830 6836 w 10 R f ( attempted \(the step)3 812( is the function reduction predicted for the last step taken or)11 2470(\320 V\(7\))1 338 3 1420 6836 t ( quantity PRELDF described in \2476b is)6 1810( The)1 252(corresponding to V\(DSTNRM\)\).)2 1408 3 1570 6956 t (V\(PREDUC\))1570 7086 w 13 I f (/)2135 7086 w 10 R f (max{V\(F\), V\(F0\)}.)1 781 1 2203 7086 t 10 CW f (V\(RADIUS\))830 7266 w 10 R f ( is the current trust-region radius)5 1306(\320 V\(8\))1 338 2 1420 7266 t 10 S f (d)3089 7266 w 10 R f (, described in \2477.)3 685 1 3138 7266 t ( Optimization)1 2052( 17 -)2 183( -)1 1389(October 16, 1990)2 696 4 720 7680 t cleartomark showpage saveobj restore end %%PageBoundingBox: 61 8 514 764 %%EndPage: 17 18 %%Page: 18 19 %%PageBoundingBox: (atend) DpostDict begin /saveobj save def mark 19 pagesetup 10 R f (Optimization Usage Summary)2 1216 1 720 480 t 8 R f (PORT)4548 480 w 10 R f (library)4774 480 w 10 CW f (V\(RCOND\))890 840 w 10 R f ( and only when a covariance matrix or regression diagnostic)9 2430( [regression only \320)3 802(\320 V\(53\))1 388 3 1420 840 t ( on the)2 322(array is requested] is the reciprocal of the square-root of a lower bound)12 3148 2 1570 960 t (Euclidean condition number of the final Hessian)6 2302 1 1570 1080 t 10 S f (\321)3958 1080 w 7 R f (2)4034 1040 w 10 I f (f)4093 1080 w 10 R f (\()4137 1080 w 10 I f (x)4178 1080 w 7 I f (final)4233 1040 w 10 R f ( of)1 169(\). Printing)1 492 2 4379 1080 t (V\(RCOND\))1570 1200 w 7 R f (2)2063 1160 w 10 R f (is controlled by IV\(COVPRT\) \320 see \2476a.)6 1684 1 2131 1200 t 10 CW f (V\(RELDX\))890 1380 w 10 R f ( defined by \(5.1\), of the last step taken or attempted \(the)11 2375( is the scaled length,)4 857(\320 V\(17\))1 388 3 1420 1380 t (step corresponding to V\(DSTNRM\)\).)3 1498 1 1570 1500 t 10 CW f (V\(STPPAR\))830 1680 w 10 R f ( is the step-length parameter described in \2476b.)7 1841(\320 V\(5\))1 338 2 1420 1680 t 10 B f ( V components)2 633(16. Other)1 430 2 720 1920 t 10 R f ( are)1 148( They)1 257( you should seldom have to tinker.)6 1392(There are a few obscure input V components with which)9 2273 4 970 2076 t ( to regression, and their)4 980( V\(FUZZ\), and V\(RLIMIT\) pertain only)5 1674( V\(COSMIN\),)1 613(described in \2473.15 of [2].)4 1053 4 720 2196 t ( V\(COSMIN\) = V\(47\), V\(FUZZ\) = V\(45\), and V\(RLIMIT\) = V\(46\).)10 2828( now)1 230( have changed:)2 614(subscript values)1 648 4 720 2316 t ( input V components described in \2473.15 of [2] retain their old subscript values and apply to all the)18 3933(The other)1 387 2 720 2436 t (optimization routines covered by this usage summary.)6 2162 1 720 2556 t 10 B f (17. Initial)1 437 1 720 2796 t 10 BI f (S)1182 2796 w 10 B f (matrix)1263 2796 w 10 R f ( obtain an)2 410( routines use a ``secant update'' to)6 1416( These)1 295(This section applies to regression routines only.)6 1949 4 970 2952 t (approximation)720 3072 w 10 I f (S)1334 3072 w 10 R f (to part of)2 378 1 1415 3072 t 10 S f (\321)1824 3072 w 7 R f (2)1900 3032 w 10 I f (f)1959 3072 w 10 R f ( default the)2 459( By)1 172( details in the case of nonlinear least squares.)8 1839(\320 see [1] for)3 552 4 2018 3072 t (initial)720 3192 w 10 I f (S)986 3192 w 10 R f ( it is useful to initialize)5 955( Occasionally)1 578(matrix is set to all zeros.)5 1012 3 1068 3192 t 10 I f (S)3645 3192 w 10 R f (to a finite-difference estimate of)4 1313 1 3727 3192 t ( point where the Jacobian)4 1052( is useful, for instance, if you want to start at a)11 1949( \(This)1 270(the thing it approximates.)3 1049 4 720 3312 t (matrix vanishes but)2 785 1 720 3432 t 10 S f (\321)1531 3432 w 7 R f (2)1607 3392 w 10 I f (f)1666 3432 w 10 R f ( done)1 221( can have this)3 549( You)1 223(is nonzero \320 and there exist people who want to do this!\))11 2327 4 1720 3432 t ( values to estimate the initial)5 1147(by setting IV\(INITS\) = IV\(25\) to 3 or 4; 3 means to use differences of function)15 3173 2 720 3552 t 10 I f (S)720 3672 w 10 R f (, and 4 means to use differences of gradients)8 1784 1 770 3672 t 7 R f (4)2559 3632 w 10 R f ( initial)1 261( can also supply your own)5 1051(. You)1 248 3 2602 3672 t 10 I f (S)4189 3672 w 10 R f ( proce-)1 281(matrix. The)1 493 2 4266 3672 t ( call IVSET \(DIVSET for double precision \320)7 1858( First)1 236( doing so is similar to the one described in \2474a.)10 1905(dure for)1 321 4 720 3792 t ( model \320 the one that ignores)6 1234(see \2472\), then set IV\(INITS\) to 2 \(or to 1 if you want the Gauss-Newton)14 2878 2 720 3912 t 10 I f (S)4861 3912 w 10 R f (\320)4940 3912 w ( it has set)3 396( call the appropriate optimization routine and make sure)8 2299( Next,)1 277(to be tried first\) and IV\(1\) to 13.)7 1348 4 720 4032 t ( IV\(S\) = IV\(62\) is the starting subscript in V for the lower)12 2331( Now)1 245( \(i.e., has found nothing wrong\).)5 1295(IV\(1\) to 14)2 449 4 720 4152 t (triangle of)1 415 1 720 4272 t 10 I f (S)1162 4272 w 10 R f ( your initial)2 471(. Store)1 288 2 1212 4272 t 10 I f (S)1998 4272 w 10 R f (there \(compactly by rows:)3 1051 1 2075 4272 t 10 I f (S)3178 4272 w 7 R f (1 , 1)2 98 1 3239 4292 t 10 R f (,)3345 4272 w 10 I f (S)3397 4272 w 7 R f (2 , 1)2 98 1 3458 4292 t 10 R f (,)3564 4272 w 10 I f (S)3616 4272 w 7 R f (2 , 2)2 98 1 3677 4292 t 10 R f (,)3783 4272 w 10 I f (S)3835 4272 w 7 R f (3 , 1)2 98 1 3896 4292 t 10 R f (,)4002 4272 w 10 I f (S)4054 4272 w 7 R f (3 , 2)2 98 1 4115 4292 t 10 R f (,)4221 4272 w 10 I f (S)4272 4272 w 7 R f (3 , 3)2 98 1 4333 4292 t 10 R f (. . .)2 125 1 4472 4247 t (\). Finally,)1 418 1 4622 4272 t ( will begin its algorithm.)4 987( it)1 106(call the optimization routine again:)4 1399 3 720 4392 t ( do a Monte-Carlo covariance matrix computation \(by repeatedly choosing pseudorandom)10 3809(If you)1 261 2 970 4548 t (errors, adding them to your observations, and calling the regression routine again\), then it is reasonable to)16 4320 1 720 4668 t ( subsequent calls on the regression routine be the solution from)10 2605(have the starting guess for the second and)7 1715 2 720 4788 t ( this case it is reasonable to set IV\(INITS\) to IV\(MODEL\) = IV\(5\), so that you start)16 3475( In)1 142(the previous call.)2 703 3 720 4908 t (with the)1 326 1 720 5028 t 10 I f (S)1072 5028 w 10 R f ( initial decision whether to use)5 1234(matrix and model preference \(i.e.,)4 1358 2 1148 5028 t 10 I f (S)3767 5028 w 10 R f (in computing the next step \320)5 1196 1 3844 5028 t (see [1]\) from the previous run.)5 1219 1 720 5148 t 8 S1 f (__________________)720 6980 w 8 R f ( of the possibility of setting IV\(INITS\) to 4 was omitted from the 1984)13 2253(3. Mention)1 370 2 720 7080 t 8 I f (Usage Summary)1 526 1 3363 7080 t 8 R f (.)3889 7080 w 10 R f ( 16, 1990)2 375( October)1 1677( 18 -)2 183(Optimization -)1 2085 4 720 7680 t cleartomark showpage saveobj restore end %%PageBoundingBox: 61 8 514 764 %%EndPage: 18 19 %%Page: 19 20 %%PageBoundingBox: (atend) DpostDict begin /saveobj save def mark 20 pagesetup 8 R f (PORT)720 480 w 10 R f ( Usage Summary)2 688(library Optimization)1 3406 2 946 480 t 10 B f ( values for symbolic subscripts)4 1306(18. Numerical)1 624 2 720 960 t 10 R f (The following symbolic subscripts for IV and V are discussed in the indicated sections:)13 3493 1 970 1116 t 10 S f (_ _______________________________________________________)1 2763 1 1498 1316 t 10 B f (IV symbolic subscript values, sorted alphabetically)5 2168 1 1795 1436 t 10 S f (_ _______________________________________________________)1 2763 1 1498 1456 t 10 I f ( Sections)1 483( Value)1 449( Symbol)1 505( Sections)1 483(Symbol Value)1 743 5 1548 1576 t 10 CW f (A)1548 1756 w 10 R f (98 14)1 350 1 2191 1756 t 10 CW f (NEXTIV)2985 1756 w 10 R f ( 14)1 125(46 6c,)1 416 2 3628 1756 t 10 CW f (AI)1548 1876 w 10 R f (91 14)1 350 1 2191 1876 t 10 CW f (NEXTV)2985 1876 w 10 R f ( 14)1 125(47 6c,)1 416 2 3628 1876 t 10 CW f (AM)1548 1996 w 10 R f ( 14)1 125(95 6a,)1 375 2 2191 1996 t 10 CW f (NFCALL)2985 1996 w 10 R f ( 14)1 125(6 11,)1 366 2 3678 1996 t 10 CW f (COVMAT)1548 2116 w 10 R f ( 14)1 125(26 10,)1 375 2 2191 2116 t 10 CW f (NFCOV)2985 2116 w 10 R f (52 14)1 391 1 3628 2116 t 10 CW f (COVPRT)1548 2236 w 10 R f ( 15)1 125(14 6a,)1 375 2 2191 2236 t 10 CW f (NFGCAL)2985 2236 w 10 R f (7 11)1 341 1 3678 2236 t 10 CW f (COVREQ)1548 2356 w 10 R f ( 8, 10)2 225(15 6a,)1 375 2 2191 2356 t 10 CW f (NGCALL)2985 2356 w 10 R f ( 14)1 125(30 6b,)1 416 2 3628 2356 t 10 CW f (D)1548 2476 w 10 R f ( 14)1 125(27 4d,)1 375 2 2191 2476 t 10 CW f (NGCOV)2985 2476 w 10 R f (53 14)1 391 1 3628 2476 t 10 CW f (DRADPR)1548 2596 w 10 R f (101 6a)1 400 1 2141 2596 t 10 CW f (NITER)2985 2596 w 10 R f (31 14)1 391 1 3628 2596 t 10 CW f (DTOL)1548 2716 w 10 R f (59 4d)1 350 1 2191 2716 t 10 CW f (OUTLEV)2985 2716 w 10 R f (19 6a)1 391 1 3628 2716 t 10 CW f (DTYPE)1548 2836 w 10 R f ( 4c)1 119(16 3,)1 375 2 2191 2836 t 10 CW f (PARPRT)2985 2836 w 10 R f (20 6a)1 391 1 3628 2836 t 10 CW f (G)1548 2956 w 10 R f (28 14)1 350 1 2191 2956 t 10 CW f (PC)2985 2956 w 10 R f (90 14)1 391 1 3628 2956 t 10 CW f (INITS)1548 3076 w 10 R f ( 17)1 125(25 3,)1 375 2 2191 3076 t 10 CW f (PRUNIT)2985 3076 w 10 R f ( 6a)1 119(21 2,)1 416 2 3628 3076 t 10 CW f (LASTIV)1548 3196 w 10 R f ( 6c, 14)2 269(44 2,)1 375 2 2191 3196 t 10 CW f (RDREQ)2985 3196 w 10 R f (57 10)1 391 1 3628 3196 t 10 CW f (LASTV)1548 3316 w 10 R f ( 6c, 14)2 269(45 2,)1 375 2 2191 3316 t 10 CW f (REGD)2985 3316 w 10 R f (67 10)1 391 1 3628 3316 t 10 CW f (MC)1548 3436 w 10 R f (83 14)1 350 1 2191 3436 t 10 CW f (S)2985 3436 w 10 R f (62 17)1 391 1 3628 3436 t 10 CW f (ME)1548 3556 w 10 R f (86 14)1 350 1 2191 3556 t 10 CW f (SOLPRT)2985 3556 w 10 R f ( 14)1 125(22 6a,)1 416 2 3628 3556 t 10 CW f (ME1)1548 3676 w 10 R f (87 14)1 350 1 2191 3676 t 10 CW f (STATPR)2985 3676 w 10 R f ( 14)1 125(23 6b,)1 416 2 3628 3676 t 10 CW f (MODE)1548 3796 w 10 R f (35 9)1 350 1 2191 3796 t 10 CW f (SUSED)2985 3796 w 10 R f (64 14)1 391 1 3628 3796 t 10 CW f (MODEL)1548 3916 w 10 R f (5 17)1 300 1 2241 3916 t 10 CW f (TOOBIG)2985 3916 w 10 R f (2 11)1 341 1 3678 3916 t 10 CW f (MXFCAL)1548 4036 w 10 R f ( 5)1 75(17 3,)1 375 2 2191 4036 t 10 CW f (X0PRT)2985 4036 w 10 R f (24 6a)1 391 1 3628 4036 t 10 CW f (MXITER)1548 4156 w 10 R f ( 3, 5)2 175(18 1,)1 375 2 2191 4156 t 10 S f ( \347)1 -2763(_ _______________________________________________________)1 2763 2 1498 4176 t (\347)1498 4116 w (\347)1498 4016 w (\347)1498 3916 w (\347)1498 3816 w (\347)1498 3716 w (\347)1498 3616 w (\347)1498 3516 w (\347)1498 3416 w (\347)1498 3316 w (\347)1498 3216 w (\347)1498 3116 w (\347)1498 3016 w (\347)1498 2916 w (\347)1498 2816 w (\347)1498 2716 w (\347)1498 2616 w (\347)1498 2516 w (\347)1498 2416 w (\347)1498 2316 w (\347)1498 2216 w (\347)1498 2116 w (\347)1498 2016 w (\347)1498 1916 w (\347)1498 1816 w (\347)1498 1716 w (\347)1498 1616 w (\347)1498 1516 w (\347)1498 1416 w (\347)2910 4176 w (\347)2910 4156 w (\347)2910 4056 w (\347)2910 3956 w (\347)2910 3856 w (\347)2910 3756 w (\347)2910 3656 w (\347)2910 3556 w (\347)2910 3456 w (\347)2910 3356 w (\347)2910 3256 w (\347)2910 3156 w (\347)2910 3056 w (\347)2910 2956 w (\347)2910 2856 w (\347)2910 2756 w (\347)2910 2656 w (\347)2910 2556 w (\347)2910 2456 w (\347)2910 2356 w (\347)2910 2256 w (\347)2910 2156 w (\347)2910 2056 w (\347)2910 1956 w (\347)2910 1856 w (\347)2910 1756 w (\347)2910 1656 w (\347)2910 1556 w (\347)4261 4176 w (\347)4261 4116 w (\347)4261 4016 w (\347)4261 3916 w (\347)4261 3816 w (\347)4261 3716 w (\347)4261 3616 w (\347)4261 3516 w (\347)4261 3416 w (\347)4261 3316 w (\347)4261 3216 w (\347)4261 3116 w (\347)4261 3016 w (\347)4261 2916 w (\347)4261 2816 w (\347)4261 2716 w (\347)4261 2616 w (\347)4261 2516 w (\347)4261 2416 w (\347)4261 2316 w (\347)4261 2216 w (\347)4261 2116 w (\347)4261 2016 w (\347)4261 1916 w (\347)4261 1816 w (\347)4261 1716 w (\347)4261 1616 w (\347)4261 1516 w (\347)4261 1416 w (_ _________________________________________________________)1 2869 1 1445 4436 t 10 B f (V symbolic subscript values, sorted alphabetically)5 2129 1 1815 4556 t 10 S f (_ _________________________________________________________)1 2869 1 1445 4576 t 10 I f ( Sections)1 483( Value)1 449( Sections Symbol)2 927(Symbol Value)1 743 4 1495 4696 t 10 CW f (AFCTOL)1495 4876 w 10 R f ( 5)1 75(31 3,)1 416 2 2138 4876 t 10 CW f (FUZZ)2871 4876 w 10 R f (45 16)1 350 1 3514 4876 t 10 CW f (COSMIN)1495 4996 w 10 R f (47 16)1 391 1 2138 4996 t 10 CW f (LMAX0)2871 4996 w 10 R f (35 7)1 350 1 3514 4996 t 10 CW f (D0INIT)1495 5116 w 10 R f (40 4a)1 391 1 2138 5116 t 10 CW f (LMAXS)2871 5116 w 10 R f (36 5)1 350 1 3514 5116 t 10 CW f (DELTA0)1495 5236 w 10 R f ( 9)1 75(44 8,)1 416 2 2138 5236 t 10 CW f (NREDUC)2871 5236 w 10 R f (6 15)1 300 1 3564 5236 t 10 CW f (DFAC)1495 5356 w 10 R f (41 4a)1 391 1 2138 5356 t 10 CW f (PREDUC)2871 5356 w 10 R f ( 15)1 125(7 9,)1 325 2 3564 5356 t 10 CW f (DGNORM)1495 5476 w 10 R f (1 15)1 341 1 2188 5476 t 10 CW f (RADIUS)2871 5476 w 10 R f (8 15)1 300 1 3564 5476 t 10 CW f (DINIT)1495 5596 w 10 R f (38 4b)1 391 1 2138 5596 t 10 CW f (RCOND)2871 5596 w 10 R f (53 15)1 350 1 3514 5596 t 10 CW f (DLTFDC)1495 5716 w 10 R f ( 9)1 75(42 8,)1 416 2 2138 5716 t 10 CW f (RELDX)2871 5716 w 10 R f (17 15)1 350 1 3514 5716 t 10 CW f (DLTFDJ)1495 5836 w 10 R f ( 9)1 75(43 8,)1 416 2 2138 5836 t 10 CW f (RFCTOL)2871 5836 w 10 R f ( 5, 9)2 175(32 3,)1 375 2 3514 5836 t 10 CW f (DSTNRM)1495 5956 w 10 R f (2 15)1 341 1 2188 5956 t 10 CW f (RLIMIT)2871 5956 w 10 R f (46 16)1 350 1 3514 5956 t 10 CW f (DTINIT)1495 6076 w 10 R f (39 4d)1 391 1 2138 6076 t 10 CW f (SCTOL)2871 6076 w 10 R f ( 6b, 9, 15)3 375(37 5,)1 375 2 3514 6076 t 10 CW f (ETA0)1495 6196 w 10 R f ( 9)1 75(42 8,)1 416 2 2138 6196 t 10 CW f (STPPAR)2871 6196 w 10 R f (5 15)1 300 1 3564 6196 t 10 CW f (F)1495 6316 w 10 R f ( 15)1 125(10 10,)1 416 2 2138 6316 t 10 CW f (XCTOL)2871 6316 w 10 R f ( 5)1 75(33 3,)1 375 2 3514 6316 t 10 CW f (F0)1495 6436 w 10 R f ( 15)1 125(13 9,)1 416 2 2138 6436 t 10 CW f (XFTOL)2871 6436 w 10 R f (34 5)1 350 1 3514 6436 t 10 S f ( \347)1 -2869(_ _________________________________________________________)1 2869 2 1445 6456 t (\347)1445 6436 w (\347)1445 6336 w (\347)1445 6236 w (\347)1445 6136 w (\347)1445 6036 w (\347)1445 5936 w (\347)1445 5836 w (\347)1445 5736 w (\347)1445 5636 w (\347)1445 5536 w (\347)1445 5436 w (\347)1445 5336 w (\347)1445 5236 w (\347)1445 5136 w (\347)1445 5036 w (\347)1445 4936 w (\347)1445 4836 w (\347)1445 4736 w (\347)1445 4636 w (\347)1445 4536 w (\347)2796 6456 w (\347)2796 6376 w (\347)2796 6276 w (\347)2796 6176 w (\347)2796 6076 w (\347)2796 5976 w (\347)2796 5876 w (\347)2796 5776 w (\347)2796 5676 w (\347)2796 5576 w (\347)2796 5476 w (\347)2796 5376 w (\347)2796 5276 w (\347)2796 5176 w (\347)2796 5076 w (\347)2796 4976 w (\347)2796 4876 w (\347)2796 4776 w (\347)2796 4676 w (\347)4314 6456 w (\347)4314 6436 w (\347)4314 6336 w (\347)4314 6236 w (\347)4314 6136 w (\347)4314 6036 w (\347)4314 5936 w (\347)4314 5836 w (\347)4314 5736 w (\347)4314 5636 w (\347)4314 5536 w (\347)4314 5436 w (\347)4314 5336 w (\347)4314 5236 w (\347)4314 5136 w (\347)4314 5036 w (\347)4314 4936 w (\347)4314 4836 w (\347)4314 4736 w (\347)4314 4636 w (\347)4314 4536 w 10 R f ( Optimization)1 2052( 19 -)2 183( -)1 1389(October 16, 1990)2 696 4 720 7680 t cleartomark showpage saveobj restore end %%PageBoundingBox: 61 8 514 764 %%EndPage: 19 20 %%Page: 20 21 %%PageBoundingBox: (atend) DpostDict begin /saveobj save def mark 21 pagesetup 10 R f (Optimization Usage Summary)2 1216 1 720 480 t 8 R f (PORT)4548 480 w 10 R f (library)4774 480 w 10 S f (_ _______________________________________________________)1 2780 1 1490 800 t 10 B f (IV symbolic subscript values, sorted numerically)5 2078 1 1841 920 t 10 S f (_ _______________________________________________________)1 2780 1 1490 940 t 10 I f ( Symbol Sections)2 993( Value)1 400(Value Symbol Sections)2 1226 3 1540 1060 t 10 R f (2)1723 1240 w 10 CW f (TOOBIG)1923 1240 w 10 R f (11 35)1 733 1 2433 1240 t 10 CW f (MODE)3316 1240 w 10 R f (9)3876 1240 w (5)1723 1360 w 10 CW f (MODEL)1923 1360 w 10 R f (17 44)1 733 1 2433 1360 t 10 CW f (LASTIV)3316 1360 w 10 R f (2, 6c, 14)2 344 1 3876 1360 t (6)1723 1480 w 10 CW f (NFCALL)1923 1480 w 10 R f ( 45)1 483(11, 14)1 250 2 2433 1480 t 10 CW f (LASTV)3316 1480 w 10 R f (2, 6c, 14)2 344 1 3876 1480 t (7)1723 1600 w 10 CW f (NFGCAL)1923 1600 w 10 R f (11 46)1 733 1 2433 1600 t 10 CW f (NEXTIV)3316 1600 w 10 R f (6c, 14)1 244 1 3832 1600 t (14)1673 1720 w 10 CW f (COVPRT)1923 1720 w 10 R f ( 47)1 483(6a, 15)1 244 2 2439 1720 t 10 CW f (NEXTV)3316 1720 w 10 R f (6c, 14)1 244 1 3832 1720 t (15)1673 1840 w 10 CW f (COVREQ)1923 1840 w 10 R f ( 52)1 383(6a, 8, 10)2 344 2 2439 1840 t 10 CW f (NFCOV)3316 1840 w 10 R f (14)3826 1840 w (16)1673 1960 w 10 CW f (DTYPE)1923 1960 w 10 R f ( 53)1 489(3, 4c)1 194 2 2483 1960 t 10 CW f (NGCOV)3316 1960 w 10 R f (14)3826 1960 w (17)1673 2080 w 10 CW f (MXFCAL)1923 2080 w 10 R f ( 57)1 533(3, 5)1 150 2 2483 2080 t 10 CW f (RDREQ)3316 2080 w 10 R f (10)3826 2080 w (18)1673 2200 w 10 CW f (MXITER)1923 2200 w 10 R f ( 59)1 433(1, 3, 5)2 250 2 2483 2200 t 10 CW f (DTOL)3316 2200 w 10 R f (4d)3826 2200 w (19)1673 2320 w 10 CW f (OUTLEV)1923 2320 w 10 R f (6a 62)1 727 1 2439 2320 t 10 CW f (S)3316 2320 w 10 R f (17)3826 2320 w (20)1673 2440 w 10 CW f (PARPRT)1923 2440 w 10 R f (6a 64)1 727 1 2439 2440 t 10 CW f (SUSED)3316 2440 w 10 R f (14)3826 2440 w (21)1673 2560 w 10 CW f (PRUNIT)1923 2560 w 10 R f ( 67)1 489(2, 6a)1 194 2 2483 2560 t 10 CW f (REGD)3316 2560 w 10 R f (10)3826 2560 w (22)1673 2680 w 10 CW f (SOLPRT)1923 2680 w 10 R f ( 83)1 483(6a, 14)1 244 2 2439 2680 t 10 CW f (MC)3316 2680 w 10 R f (14)3826 2680 w (23)1673 2800 w 10 CW f (STATPR)1923 2800 w 10 R f ( 86)1 483(6b, 14)1 250 2 2433 2800 t 10 CW f (ME)3316 2800 w 10 R f (14)3826 2800 w (24)1673 2920 w 10 CW f (X0PRT)1923 2920 w 10 R f (6a 87)1 727 1 2439 2920 t 10 CW f (ME1)3316 2920 w 10 R f (14)3826 2920 w (25)1673 3040 w 10 CW f (INITS)1923 3040 w 10 R f ( 90)1 483(3, 17)1 200 2 2483 3040 t 10 CW f (PC)3316 3040 w 10 R f (14)3826 3040 w (26)1673 3160 w 10 CW f (COVMAT)1923 3160 w 10 R f ( 91)1 483(10, 14)1 250 2 2433 3160 t 10 CW f (AI)3316 3160 w 10 R f (14)3826 3160 w (27)1673 3280 w 10 CW f (D)1923 3280 w 10 R f ( 95)1 483(4d, 14)1 250 2 2433 3280 t 10 CW f (AM)3316 3280 w 10 R f (6a, 14)1 244 1 3832 3280 t (28)1673 3400 w 10 CW f (G)1923 3400 w 10 R f (14 98)1 733 1 2433 3400 t 10 CW f (A)3316 3400 w 10 R f (14)3826 3400 w (30)1673 3520 w 10 CW f (NGCALL)1923 3520 w 10 R f ( 101)1 483(6b, 14)1 250 2 2433 3520 t 10 CW f (DRADPR)3316 3520 w 10 R f (6a)3832 3520 w (31)1673 3640 w 10 CW f (NITER)1923 3640 w 10 R f (14)2433 3640 w 10 S f ( \347)1 -2780(_ _______________________________________________________)1 2780 2 1490 3660 t (\347)1490 3600 w (\347)1490 3500 w (\347)1490 3400 w (\347)1490 3300 w (\347)1490 3200 w (\347)1490 3100 w (\347)1490 3000 w (\347)1490 2900 w (\347)1490 2800 w (\347)1490 2700 w (\347)1490 2600 w (\347)1490 2500 w (\347)1490 2400 w (\347)1490 2300 w (\347)1490 2200 w (\347)1490 2100 w (\347)1490 2000 w (\347)1490 1900 w (\347)1490 1800 w (\347)1490 1700 w (\347)1490 1600 w (\347)1490 1500 w (\347)1490 1400 w (\347)1490 1300 w (\347)1490 1200 w (\347)1490 1100 w (\347)1490 1000 w (\347)1490 900 w (\347)2858 3660 w (\347)2858 3640 w (\347)2858 3540 w (\347)2858 3440 w (\347)2858 3340 w (\347)2858 3240 w (\347)2858 3140 w (\347)2858 3040 w (\347)2858 2940 w (\347)2858 2840 w (\347)2858 2740 w (\347)2858 2640 w (\347)2858 2540 w (\347)2858 2440 w (\347)2858 2340 w (\347)2858 2240 w (\347)2858 2140 w (\347)2858 2040 w (\347)2858 1940 w (\347)2858 1840 w (\347)2858 1740 w (\347)2858 1640 w (\347)2858 1540 w (\347)2858 1440 w (\347)2858 1340 w (\347)2858 1240 w (\347)2858 1140 w (\347)2858 1040 w (\347)4270 3660 w (\347)4270 3600 w (\347)4270 3500 w (\347)4270 3400 w (\347)4270 3300 w (\347)4270 3200 w (\347)4270 3100 w (\347)4270 3000 w (\347)4270 2900 w (\347)4270 2800 w (\347)4270 2700 w (\347)4270 2600 w (\347)4270 2500 w (\347)4270 2400 w (\347)4270 2300 w (\347)4270 2200 w (\347)4270 2100 w (\347)4270 2000 w (\347)4270 1900 w (\347)4270 1800 w (\347)4270 1700 w (\347)4270 1600 w (\347)4270 1500 w (\347)4270 1400 w (\347)4270 1300 w (\347)4270 1200 w (\347)4270 1100 w (\347)4270 1000 w (\347)4270 900 w (_ _________________________________________________________)1 2869 1 1445 3920 t 10 B f (V symbolic subscript values, sorted numerically)5 2039 1 1860 4040 t 10 S f (_ _________________________________________________________)1 2869 1 1445 4060 t 10 I f ( Symbol Sections)2 993( Value)1 383(Value Symbol Sections)2 1226 3 1495 4180 t 10 R f (1)1678 4360 w 10 CW f (DGNORM)1878 4360 w 10 R f (15 36)1 700 1 2404 4360 t 10 CW f (LMAXS)3254 4360 w 10 R f (5)3814 4360 w (2)1678 4480 w 10 CW f (DSTNRM)1878 4480 w 10 R f (15 37)1 700 1 2404 4480 t 10 CW f (SCTOL)3254 4480 w 10 R f (5, 6b, 9, 15)3 450 1 3814 4480 t (5)1678 4600 w 10 CW f (STPPAR)1878 4600 w 10 R f (15 38)1 700 1 2404 4600 t 10 CW f (DINIT)3254 4600 w 10 R f (4b)3764 4600 w (6)1678 4720 w 10 CW f (NREDUC)1878 4720 w 10 R f (15 39)1 700 1 2404 4720 t 10 CW f (DTINIT)3254 4720 w 10 R f (4d)3764 4720 w (7)1678 4840 w 10 CW f (PREDUC)1878 4840 w 10 R f ( 40)1 450(9, 15)1 200 2 2454 4840 t 10 CW f (D0INIT)3254 4840 w 10 R f (4a)3770 4840 w (8)1678 4960 w 10 CW f (RADIUS)1878 4960 w 10 R f (15 41)1 700 1 2404 4960 t 10 CW f (DFAC)3254 4960 w 10 R f (4a)3770 4960 w (10)1628 5080 w 10 CW f (F)1878 5080 w 10 R f ( 42)1 450(10, 15)1 250 2 2404 5080 t 10 CW f (DLTFDC)3254 5080 w 10 R f (8, 9)1 150 1 3814 5080 t (13)1628 5200 w 10 CW f (F0)1878 5200 w 10 R f ( 42)1 450(9, 15)1 200 2 2454 5200 t 10 CW f (ETA0)3254 5200 w 10 R f (8, 9)1 150 1 3814 5200 t (17)1628 5320 w 10 CW f (RELDX)1878 5320 w 10 R f (15 43)1 700 1 2404 5320 t 10 CW f (DLTFDJ)3254 5320 w 10 R f (8, 9)1 150 1 3814 5320 t (31)1628 5440 w 10 CW f (AFCTOL)1878 5440 w 10 R f ( 44)1 500(3, 5)1 150 2 2454 5440 t 10 CW f (DELTA0)3254 5440 w 10 R f (8, 9)1 150 1 3814 5440 t (32)1628 5560 w 10 CW f (RFCTOL)1878 5560 w 10 R f ( 45)1 400(3, 5, 9)2 250 2 2454 5560 t 10 CW f (FUZZ)3254 5560 w 10 R f (16)3764 5560 w (33)1628 5680 w 10 CW f (XCTOL)1878 5680 w 10 R f ( 46)1 500(3, 5)1 150 2 2454 5680 t 10 CW f (RLIMIT)3254 5680 w 10 R f (16)3764 5680 w (34)1628 5800 w 10 CW f (XFTOL)1878 5800 w 10 R f (5 47)1 650 1 2454 5800 t 10 CW f (COSMIN)3254 5800 w 10 R f (16)3764 5800 w (35)1628 5920 w 10 CW f (LMAX0)1878 5920 w 10 R f (7 53)1 650 1 2454 5920 t 10 CW f (RCOND)3254 5920 w 10 R f (15)3764 5920 w 10 S f ( \347)1 -2869(_ _________________________________________________________)1 2869 2 1445 5940 t (\347)1445 5920 w (\347)1445 5820 w (\347)1445 5720 w (\347)1445 5620 w (\347)1445 5520 w (\347)1445 5420 w (\347)1445 5320 w (\347)1445 5220 w (\347)1445 5120 w (\347)1445 5020 w (\347)1445 4920 w (\347)1445 4820 w (\347)1445 4720 w (\347)1445 4620 w (\347)1445 4520 w (\347)1445 4420 w (\347)1445 4320 w (\347)1445 4220 w (\347)1445 4120 w (\347)1445 4020 w (\347)2796 5940 w (\347)2796 5860 w (\347)2796 5760 w (\347)2796 5660 w (\347)2796 5560 w (\347)2796 5460 w (\347)2796 5360 w (\347)2796 5260 w (\347)2796 5160 w (\347)2796 5060 w (\347)2796 4960 w (\347)2796 4860 w (\347)2796 4760 w (\347)2796 4660 w (\347)2796 4560 w (\347)2796 4460 w (\347)2796 4360 w (\347)2796 4260 w (\347)2796 4160 w (\347)4314 5940 w (\347)4314 5920 w (\347)4314 5820 w (\347)4314 5720 w (\347)4314 5620 w (\347)4314 5520 w (\347)4314 5420 w (\347)4314 5320 w (\347)4314 5220 w (\347)4314 5120 w (\347)4314 5020 w (\347)4314 4920 w (\347)4314 4820 w (\347)4314 4720 w (\347)4314 4620 w (\347)4314 4520 w (\347)4314 4420 w (\347)4314 4320 w (\347)4314 4220 w (\347)4314 4120 w (\347)4314 4020 w 10 B f ( variations)1 453(19. Fortran)1 513 2 720 6240 t 10 R f ( code covered by this usage summary may be converted from)10 2460(The source)1 440 2 970 6396 t 7 R f (4)3875 6356 w 10 R f (Fortran 77 to Fortran 66 by)5 1096 1 3944 6396 t ( blank the ``)3 524(changing to a)2 566 2 720 6516 t 10 CW f (C)1810 6516 w 10 R f ('' in column 1 of lines that come after a ``)10 1804 1 1870 6516 t 10 CW f (C/6)3674 6516 w 10 R f ('' line and before a line that)6 1186 1 3854 6516 t (begins ``)1 359 1 720 6636 t 10 CW f (C/7)1079 6636 w 10 R f ( lines between a line that begins ``)7 1423('' and by commenting out all)5 1198 2 1259 6636 t 10 CW f (C/7)3880 6636 w 10 R f ('' and a line that begins)5 980 1 4060 6636 t (``)720 6756 w 10 CW f (C/)786 6756 w 10 R f ( example, change)2 695(''. For)1 280 2 906 6756 t 8 S1 f (__________________)720 6880 w 8 R f ( 1984)1 181(4. The)1 225 2 720 6980 t 8 I f (Usage Summary)1 528 1 1147 6980 t 8 R f ( tapes distributed since mid-1990)4 1064( PORT)1 248(described conversion to Fortran 77 from Fortran 66.)7 1671 3 1697 6980 t (have been in Fortran 77 form, and the PORT source available from)11 2135 1 720 7080 t 8 I f (netlib)2875 7080 w 8 R f (has always been in Fortran 77 form.)6 1147 1 3076 7080 t 10 R f ( 16, 1990)2 375( October)1 1677( 20 -)2 183(Optimization -)1 2085 4 720 7680 t cleartomark showpage saveobj restore end %%PageBoundingBox: 61 8 514 764 %%EndPage: 20 21 %%Page: 21 22 %%PageBoundingBox: (atend) DpostDict begin /saveobj save def mark 22 pagesetup 8 R f (PORT)720 480 w 10 R f ( Usage Summary)2 688(library Optimization)1 3406 2 946 480 t 10 CW f (C/6)970 840 w ( A/98/, AI/91/, AM/95/, MC/83/, ME/86/, ME1/87/, PC/90/,)7 3360(C DATA)1 600 2 970 960 t ( SOLPRT/22/)1 660( PRUNIT/21/,)1 960(C 1)1 360 3 970 1080 t (C/7)970 1200 w (PARAMETER \(A=98, AI=91, AM=95, MC=83, ME=86, ME1=87, PC=90,)7 3540 1 1330 1320 t ( SOLPRT=22\))1 660(1 PRUNIT=21,)1 1320 2 1270 1440 t (C/)970 1560 w 10 R f (to)720 1740 w 10 CW f (C/6)970 1920 w (DATA A/98/, AI/91/, AM/95/, MC/83/, ME/86/, ME1/87/, PC/90/,)7 3600 1 1330 2040 t ( SOLPRT/22/)1 660(1 PRUNIT/21/,)1 1020 2 1270 2160 t (C/7)970 2280 w ( \(A=98, AI=91, AM=95, MC=83, ME=86, ME1=87, PC=90,)7 3000(C PARAMETER)1 900 2 970 2400 t ( SOLPRT=22\))1 660( PRUNIT=21,)1 1260(C 1)1 360 3 970 2520 t (C/)970 2640 w 10 R f ( convert some PARAMETER statements to)5 1781( changes)1 353( These)1 295(Some modules have several sets of such lines.)7 1891 4 720 2820 t ( numeric variables, change quoted strings in DATA)7 2133(DATA statements, turn CHARACTER variables into)5 2187 2 720 2940 t ( remove SAVE statements that may save a bit of execution time on)12 2728(statements into Hollerith constants, and)4 1592 2 720 3060 t (some computers.)1 677 1 720 3180 t 10 B f (References)720 3420 w 10 R f ( Welsch, ``An Adaptive Nonlinear Least-Squares Algorithm'',)6 2536( Dennis, Jr., D.M. Gay, and R.E.)6 1334([1] J.E.)1 450 3 720 3696 t 10 I f (ACM Trans. Math. Software)3 1137 1 1270 3816 t 10 B f (7)2432 3816 w 10 R f (\(1981\), pp. 348\261368.)2 841 1 2507 3816 t ( \320 An Adaptive Nonlinear)4 1087( NL2SOL)1 422( Dennis, Jr., D.M. Gay, and R.E. Welsch, ``Algorithm 573.)9 2361([2] J.E.)1 450 4 720 4056 t (Least-Squares Algorithm'',)1 1098 1 1270 4176 t 10 I f (ACM Trans. Math. Software)3 1137 1 2393 4176 t 10 B f (7)3555 4176 w 10 R f (\(1981\), pp. 369\261383.)2 841 1 3630 4176 t ( Gay, ``Computing Optimal Locally Constrained Steps'',)6 2414([3] D.M.)1 511 2 720 4416 t 10 I f ( Comput.)1 390(SIAM J. Sci. Statist.)3 860 2 3692 4416 t 10 B f (2)4990 4416 w 10 R f (\(1981\), pp. 186\261197.)2 841 1 1270 4536 t ( for Unconstrained Minimization Using a Model/Trust-)6 2299( Subroutines)1 543( 611.)1 215( Gay, ``Algorithm)2 752([4] D.M.)1 511 5 720 4776 t (Region Approach'',)1 798 1 1270 4896 t 10 I f (ACM Trans. Math. Software)3 1137 1 2093 4896 t 10 B f (9)3255 4896 w 10 R f (\(1983\), pp. 369\261383.)2 841 1 3330 4896 t ( Gill, W. Murray, and M.H. Wright,)6 1437([5] P.E.)1 467 2 720 5136 t 10 I f (Practical Optimization)1 920 1 2649 5136 t 10 R f (, Academic Press, London, 1981.)4 1326 1 3569 5136 t ( Stewart, ``A Modification of Davidon's Minimization Method to Accept Difference Approxi-)11 3804([6] G.W.)1 516 2 720 5376 t (mations of Derivatives'',)2 1001 1 1270 5496 t 10 I f (J. Assoc. Comput. Mach.)3 996 1 2296 5496 t 10 B f (14)3317 5496 w 10 R f (\(1967\), pp. 72\26183.)2 741 1 3442 5496 t ( Optimization)1 2052( 21 -)2 183( -)1 1389(October 16, 1990)2 696 4 720 7680 t cleartomark showpage saveobj restore end %%PageBoundingBox: 61 8 514 764 %%EndPage: 21 22 %%Trailer DpostDict begin done end %%Pages: 22 %%DocumentFonts: Times-BoldItalic Courier Times-Bold Times-Italic Times-Roman Times-Roman Symbol