Supporting information for Ind. Eng. Chem. Proc. Des. Dev., 1976, 15(3), , DOI: /i260059a003

372-377

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Copyright © 1976 American Chemical Society Supporting information for Ind. Eng. Chem. Proc. Des. Dev., 1976, 15(3), 372 – 377, DOI: 10.1021/i260059a003

377-

SuRRnuTI<-t ( & . ,

_

?, , AV ,*,

*S0L

, , AtID

,

,

IPRNT)

TMP^ICTT

REtiL*8(A-H,n-Z)#!^TEGER*ti(l»N)

C C "

TH]S PROGRAM

COHPUTES

PHYSICAL

AND

CHEMICAL

' J

L

I RRIUV

RY

C

V7MU

-'G

TmE

_GIBBS

_FREE

_ENERGY

C

COy^ONi/A/Z

(

IS)

,FL ( 1

5)

,Fv(

15)

.Fn(

1

5)

,

AMUC

15)

,

AK^Sf

1

S)

COu^ON/B/

IpuRE (3)

#

Ni UR

#

IPHASE

,<

CO^^QK'/C/^f' ,

9(

15),A

f 5,15)

COmmanvD/MAXC

F F A_L r;I R

s

DI^EMSTON PBE

ST

c Zt5)

,0(05) ,0(4 32

0)

,X(15)

,

(15),*

U5),AS(

15,

1SH

*

TRACE(15).PIC15).V(15)

C

C *' «

U^R

R DF

C0vPQN;CN!T5

C v -

M'~PER

OF ATOv

JC

SPECIES

OR

REACT I

fj*-

GRCupS

C

"I^MASE

-

MJh-RER

OF

PWASES

C Mpi-tfF · .\U -»

f

R OF

°UR

PHASES

C

TDi'Rf

-

iHf

CORRESPONOING

PIJRE

CC'HpnhvE^Ts

C

vi; .

'^ODIFIEO

STA\HAQn

STATE

CHH'ICaL

F_{\ A}L

,

USUALLY

C 1 HP

_FREE

_ENERGY

_OF

_formation

_{PER «Ou DIVIDED BY}

_k*T,

C

IF

- QR vn

REACTION, ,

C

PL

-

FIRST

PhASE

fijgacITV

C Fv -

S Cn^

PSASE

FU6AC1TY

C Fw ·

third

PmaSE

fugacity

C 7

_{-INITIAL mqlfs}

r _{A( ,J)} - MJv R OF

ATOmS

OR

REACTION

GROUPS

OF

SPECIF

I

C I^

COMPONENT

J

C

F·

IF

C*EMICAL

REACTION

OCCURS,

ALL

ATO^S

np

C

REACT

ION GROUPS

SHQULh

BE

INTRODUCED

1

*

_THE

C

CIRST

"

_COMPONENTS

C c*********************************************************************** nn

_{2 1}

=₁ ,

ARHS(

=

100

( )=0,

(!)=0,

·" ( I

)

=

_.

(

=

,

2

CONTINUE

K:TPHASE-NPURfc

IF

_(K.EQ.

1

_{.AND.K.fcQ.O)}

GO

TU tiO

if

_c<,Ec,a)

" ' TF

_C^.FQ.i)

M?sj=

_2*h

IF

_{(", , )}

GO

TO

16

no

u

1=1.w

DO

J=),M

u

AS(I,J)=A(I,J)

00

33

1=

1,'·'

p(I)=0.

00

3ti

J

= _{1 ,} *

2'i

A(

J

)=f5(I)tAf

j,

j)*z(J)

33 CO^-' V'NE

00 23

1=1^

00

23

J=1

23

A(I,J)=A(I,JV/B(I)

CALL

v'Ay ^ 2 *_^»

6?,

6**. 18

CALL I'PIRJ (A, ARHS,«,NJ)

n-1 20 1 = 1, '^v ^ 3 7 7 - ™2

00560 00570

bll , ?o p « F S T ( n = - 5 . 00580

6 5 , CALL. PP'.PL(N)M,PHF.ST,P,G,0,1 , 1 D - 6 . « A Y ,0, 0 ) 00590 66. If ( IPOW7 .FQ, 1 ) WRITf (10*,5) ( z c n , i = i,N) 00591

6 7 . 5 F09HA1 (' Z = S ( 7 F ! 1 5 , 6 ) ) 00592 6 8 , TF (^ayc.LT.MAy.AK'O.K.MEf.l) GO TO 3 00600 6 « . IF (K.FQ.l) CALL L A G R X S ( U , M , A S . Z , A K I J , F U I P U S E . I T R A C E , 1 0 - 6 , P i , 00601 7 0 . * 1PRNT> ? GO TO uo 00602 7i . HE!. = 10-2 00610 7?. C AI L [ ; T K S £ * ( ^ , GIBBS, 3REST. 1 000, I D - 11 . D E L , ,618) 00615 73, 3 r,p Tn (ao,<M#o°) K 00620 70, At TQsO," 0 0630 7 5 . nn 4? 1 = 1, ^ 00640 7 6 . JF (I IPUPF ( i ) ) Gn TO 4 ? 00650 77, TF C T, F fo, IP !j R E (2)) r,o TO (12 00660 7ft, IF (T. F0.iPuRhC3)) Gn TP 4? ₀₀₆₆₅ 7 9 . _{A L ! K = A L I ^ • Z ( T ) 00670} 8ft • ^2 CQVT T fvUfc* 00680' B1 , TF ( f - P ! i ^ : , G Etn A vAP = 7( I PURE ( 1 ) ) 00690

e?. TF (VPHRF.Gfc,?) ASflL = Z(IPUPEf2) ) 00700

« 3 . TF ( NP«JRK , E o , 3) *L IQi =7 (TP'IRF ( 3) 1 00705

5 'J. on (j^ 1 = 1 / * 00710

8 5 . TF (i , F Q . ] PUREC I )) en TO UT> 00720

8 6 . TF ( T ,FQ. JPURE(2)) t;n TO U3 00730"

67 . IF ( T , F o, l PuRE (3)) Gn TQ <i 3 00735

8A. y(i)=z(n/ALTQ 007^0

89. "3 CH'TTMiE 00756'

90 , V ( TPuftE(1 )) = 0, 00760

91 . T< C'vPi.RE.GF . l.ANO.Zd P>'RE C1)) ,GT,0,) Y(lPijRr( i ))-1 , 00770

9 ? , w(TPi)HF(?) 5 = 0, 00780 ^3. TF (^Pi;RF.GF;2,AND,ZfiPuRE(2)),GT.O, ) w (I PURE ( 2 )) = 1 , 00790 9 tl . V ( TPi'KF (3) )sO, 00795 9 5 , IF (vPUWF.FQ/i.AMo.ZdPURECin.GT.O,) V (I PURE ( 3 j ) = 1 , 00796 96 , CP in 'is 00800 ^7, .'j 1 ALTU=0. 008JO 9 « . AVAPsO. 00820 99, nn so j s1 , H OO830 00. IF (1 , E Q t1P i) R E ( 1 ) ) Gn TO 60 00840 01 . A V A P s A V « P * Z ( T ) « ( 1 .nHfpRt'STfnj) OO850 0?. A L T Q = A L I O f Z ( T ) * H ( P » E S T ( I ) ) 00880 0 3 , 6r> Cn-vT T >Ji.• F 00870

oa, TF ("PURE,EG,n ASOL = Z ( I P i « R E ( i n OO890

05, HQ 66 T = l , N 00900 0*. TF (T,EQ,IPURE(1)) Gn TO 66 00910 07 . y ( T ) z Z ( I > *H(0B E S T ( ! ) ) / A L l G 0 0920 Oft, V f T ) s ? C J l * ( l , - H ( P B E S T ( I ) ) ) / A V A P 00930 0 9 , 6^ CnvT T M'E 00900 10, w( TPURF(1)) = Ot 0 0950

1 1 . TF (N'PURF.Eo.l , AMn,ZfiPuRE(2n . G T . O . j w (1 PURE ( 1) ) = 1 , 00960

12, GO Tn n5 00970 1 3 . 69 AS0L=n, 00980 Id. AVAPsO, 00990 1 5 . _oiooo 1 8 , DO 6 3 T=1,N 01010 1 7 , _{JJ = I 01020} IB, AVAP=AVAP+Z(I)*H(PREST(I)) 01030

1 9 , ALTO'sA'L'in + H (PBES1 U T)) * (l > M (PBFST (I >)) *Z ( h _010UO 2 0 . 6^ ASnLsASDI.t (1 CPBESTCIT) ) j * ( 1 ,-w(PBE5T ( I ) ) W ( J) 01050

21 . nil 65 J = t , N ₀₁₀₆₀

2?. TT=I+M 01070

2 3 , VCT)=Z(J)*H(PBEST(I))/AVAP 01080

2/J, V(I)=Z(I)*H f PBEST ( 1T ) S * C 1 .-H(P8EST(U) J/ALIO 01090

"25, - "C T )=Z( ! ) * C 1 ,-H(PBEST ( I) ) ) * (1 (PBEST(H)))/ASOL _{01 Too}

2 6 . 65 COMT TMIE _{01 110}

·

Eno

_311-

^3

1

\·

FUNCTION

ACTCD(I)

1001

(

IMPLICIT

REAL*6(A-H,n-Z)

lOOli

_a_.

C

₁₀₀₃₍

5

·

C

'

!S

F _c

I

~U

$

D F Q AC

VI

Y

_COEFF

_IC

_iEtvTS

_100ti(

fee c

₁₀₀₅₍

R·

ACTCn=lD0

1

007(

9.

t?ETUPN>

_J

_008C

1^-377-0^

1 , FUNCTION GlBBS(U) ₂₀₀₁₀

2. TMPLICTT REAl.*8('A-H,ruZ) ,JMTEGER*4CI-N) 20015

3, 20020

4

t

C ₂₀₀₃₀

5 . _c THIS FUNCTION EVALUATES THE GIBBS ' FREE ENERGY 20 040

6 • c 20050 7. 20060 A . _{CnMhnN/A/zC'i5)#f} RU( J5) f Pvf 15) ,>W(15)", A^UCIS), ARHSCI5) 20070" 9 , _{Cn^0\/6/lPijRt (3) , NPURt: » I P H A S E . K 20080} 1. n, CO^^HM/C/^fN.BClS)rflf15,15) 20090

11 # r>i*.F_N!SJG'v'"U( 1 ) • YV( t5) , RHS (1 5 ), UMQM (15) ,S«(15),XL(15) 20Y60 1 2. COMMON/A!.KA/yL, ZZ2 20U0

n . •/, M - y 4 J 20120

l^t 7F (M,EO.*0') GO TO 16 20 n o

1 5 . no ioo isMMr\j 20140

1

ft.

IF (K.EQ.3) Z(1)SM(U(2*N+1-K))/B(1) 20150

17, _{TF (K.Eli. 2) 7 ( n = h(Uf Nifl-M) )/e ( I ) 201 60}

IP. T^ ( K . F P . l ) 7CI)=h(U(l-M))/B(l) 20170 1Q. i n n CO'-'T I Nt.'E 20180 20, no no i = 20190 21 . SUM=0, 20200 22. ₂₀₂₁₀ 12" StJw = SU"*A( I, J)*7< J) 20220 ?«. 1 1 * PHS(T)SARHS(TA 20230 25, CALL BAKSOLCA,PHS,UNHNI, 20240 2ft. nn a3 ! = ₂₀₂₅₀ 27, 7(1 )sU^ON'(I) 20260 2*. 1 ft nn TO (70*7t,69) K 20270 2Q. 7 0 GIBHSsO. ₂₀₂₈₀ 777=^, ₂₀₂₉₀ 31 . on 72 T=1 ₂₀₃₀₀

32. IF (1 .EG.IPt.'PEf 1 ) « O R 1 , E°, I PURE (2) •OR•J,EO, 1 PURE (3)) GO TO 72 203"! 0"

33. 7ZZ=7Z2+?CI) 20320 34, 72 CO^'T IfJUE 20330 35. nn 7s 20340' 3ft, IF <7(J).lTBn,) r' n TO 76 20350 37. r, IBHSsGIBBS* A*U( 1) * Z m 20360 38, TF (IP'.'RFin.fcO.I) GO TO 75 20370 39, JF (IPURE(2l.EO,I) GO TO 75 20380 an, TF (JPURE(3),E<3,I) Gn TO 75 ₂₀₃₈₅ 41, r,i = 7"(I)'»FL(l)/DABS(Z7Z) 20390" 42. IF ( G l . I E . 0 .) GO TP 75 20400 43. RJBBSsGlBBStZCI) *HL0G(G1) 20410 4/i, GO TO 75 20420 45. 7ft TF ( Z C T ) . G E . - l , ) GIBBS=GIBBS+lD2*OSQRT(DABS(7(I)5) 20430 ^6. IF ( 7 ( T ) , L T , - 1 , ) GIBBS=GIBRS-1D0+1D0/C(1D2)**Z(I)) ₂₀₄₄₀ 47 , ₇₅ CO^TTNUfc ₂₀₄₅₀ RETURN ₂₀₄₆₀ 4Q, _{71 7Z7=o, 20470} SO , xxv=o. 20480' 51 , 00 31 T=1,N 20490 5?, I F (T.FQ.lPliRECl )) GO TO 31 20500 53, Tisnruf i n 20510 54, T2=1,0+00-T) 20520 55, XLfI)-Tl*Z<!) 20530 5ft. YVfl")s"T'2*Z(l ) ₂₀₅₄₀ 57, 7Z7 = 7Z2 + yL(n 20550 5*. XXX=XXX+vv(J) ₂₀₅₆₀ 59, * 1 c ov T'T fvi JE 20570 60 , XXXsl.DfOO/XXX 20580 61 . 777=1.0*00/777 _2059ft

·

-^"-

377-

<"S

51

1=₁ # if

_{( ( ), . ,)}

go

ß

G'IRBS=G1*BS*AWIU!)

*Zf

1

_{(i.Eti.iPusE( ))}

si

Gl=-<L(I)*FLC!)*DAeS(ZZZ)*ACTCO(I)

G2=VVCI)*FV(I)*OABS(VXX)

TF

_{(Gi.LF.O..OR.G2.LE.O,)}

GO TO

5!

GTR9S

=

GI9BS*XL

U)*OLHGCG1) YV(I)*0LQG(G2)

GO r

_5i

"

63

IF

(Z(T)

,GE,-1

.) GI

SBS

=

GI BAS*

₁

D2*DS0PTf DAhS

_{(7 )}

₎₎

IF

_{GI8BS=GIB«S»1DO*1DO/((102)**Z(J))}

51

CO^TJkj'.iE

RETURN

t°! W W '2c,

ZZ7=0.

XXX=

_0,

no

sn

1

I I=

I*N

Tphfud))

2=·-

(ur

it))

'( )

=

* (

*tC11

=

^2*(1,-T

₁

)*Z(

I)

s-srnsM.-MW}

,-T2wm

w w ^4

₅

ts

(

I )

7Z7=7ZZ*XL(I)

so

* = < (

, D* 0 /*a*

, ^ /

ZZ7=1,no+oo/zzz

GlRRSrl.

, 50 J

= <

GlrXU(T)VL(I)*DA8S(7Z7)

G 2=

( )

*fv

(j)

*

o

a8

s (

₎

G"S-S*

( ! ) *F"·

(I

)*L>A5SU'w*)

Ip

_{(Gl.LF.0.1UQlG2,LF.0..n9,G3.LF,0,)}

GO 1 S3

GIPBSsGIRSS+xl(I)*OLORfGl)>

V(I)*OLOGCG2)*S* )

*0_{L 0}G(_G

'5)

1 Af^UC

)

*Z<

I

) GO in

50

53 TF

(7(

)

_.Gt.-l

.

) GTBRS

=

GIRBS*lR2*DSi;PT(OABS(7(!)))

TF

(7 (!

)

_,1

_T,-l

.)

GT9t>S

=

G!«RS-1

D0*1

Dn/( (1 D2)**Z

_C1))

g

r.

_C

₁₁

_£

£ »

FK^r>

-^-377-^4

.

fU^CTinf, ( ,)

₃₀₀₁₀

2,

Tv,pLTCTT

KEAL*e(A-M,n-7),

i\iiEGER*ti(l»N)

30015

C

₃₀₀₃₀

,

C ARF.1 TDARY

_ALl.UC

ft

I

0*

Fi'wCTTOM

_300*10

•3.

C

30050

ß.

IF

_(U.LT.-25.)

GO

TO 2

₃₀₀₇₀

Tt

_(",GT„25,)

GO TO

3

30080

1 * ·

Hri.D

00/(1.S

00*DF.XP(«U)

)

30090

11»

RET

U R

₃₀₁₀₀

1?.

?

_^,

₃₀₁₁₀

13.

RETURN·

₃₀₁₂₀

lti.

3

w=1.

30130

1*?.

RETURN

₃₀₁

_<10

If?.

·µ

₃₀₁₅₀

aooio

?. 00015

3. C*********************************************************************** _fl0020

c U003O

"5.""" C MAXJ SELECTS THE MAZIMUM COLUMN VALUE IN COULUMNS M4l TO * 000*0

c U0050 c****************************^*****************************^ 00060 'CQv^nNi/C/fc.K'.Bt 15) • Afi5#15) ₀₀₀₇₀ 00060 0, no io jsMf!#Ni 1 • R(J)=A(J,J) U0100 ?. _anno 3. T F ( M I , J ) . L T. n( J ) ) r,Q m 10 _«0120 a. B(J)sAd.J) ₀₀₁₃₀ 5. 10 CONTINUE _ooioo 6. 00150 7, E^-'H ani 60

SUBROUTINE UPTRI 50010

?•

IMPLICIT REAL*6(A*Hfn-2) * I * T E G F * * « C I - N ) "50015

3«

c************************************************************

***********

50020

A .

c

50030

c

UPPER TST A^GUUAl 10*- HF A v.ATRIX

5bo«o

r 50050 r********************************* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 50060

« .

DIvF*ST0\' ^ 15) , APHSC 1 5)

50070

<?.

T0l. = 1 , 0 0 - 1 5 50080 1 f' • ARMSf1 ) r A H H 5( j) / f c ( 1 ,n 50090 I

1 .

RpsAfl.O 50100 1?* nn 5 0 ,7s i , N

50110

1*. 50120 r»n 7* T = ? ,M

50130

15,

n

= I - l 50140 I f . r>n An J j s i ,n

50150

W, TFf DA^S(A( 1 r JJ) ) .LT%T0D GP TH 80 50160 1*. A«f'-:S( I)sAKHS(l)-AWHSf .K1)*A( J , J J ) 50170 10. B.BSA f I , J J ) 50180 2ft. nr; Q0 JsJJ** 50190

?1 .

Q ft A(T,J)=A(lrJ)-A(JJ,Ji*f»B 50200

??.

*», 0 50210

2^. APnSCl) = ARHSfI)/A(I.U 5O220

2'J. *3 = A f I • P 50230 2*. r>n ioo J = 1. 502O0 26.

1

00 A(T, J)=AU, J)/BB

50250

27, 70 C U T I S ' H E 5O260

?«.

5O270 50280

1.

SU^.RrijTiK-E

«_ft*

_SDL

_{C , A»HS.}

_UVP*,

_{QUI 3}

_frOOl

_o

2.

T*DL7C!

REAL*R(A«N,n-7).J^TFGFR*tiCI-v)

60015

3.

a.

C

60030

5."

C SftCK

Snl. 'T10^

DF

_MATERIAL

_AAIAMCE

_600«0 6. C 60050

7.

*.

OI^EMSIO*

6

_{( 5,}

_)5),

_ASHSM

₅₎

_{6 070} 9.

DJvfcNSTCA'·

U\n,v(iS)

600*0

in.

.'QUI

TzIQVV

60090

11.

!HPHS=ASHSCJQUIT)

60100

12.

1("JflNi(J D spAP^S

601

1 0

,

JQvr=J^l' 1

T-i

60120

Ifif

35c.

x

=_i»

₆₀₁₃₀

15.

JATBJKUIT-I

601*0

,

I&T=J6T

60150

17, ,urpn=ji *1

₆₀₁₆₀

IP.

$= 5( 6 )

60170

JQ. no 33^

JSVM

=

JATPn,

JLVI'IT

₆₀₁₈₀

20*

r»ATJ=A (

J

A 1 .

JSU*)

60190

21 .

UJ

=U^n\' (

JSU^)

60200

2?.

33n

DARHS=nARMS-DAIJ*UJ

60210

23.

\· ( JA7 1

sOiOHS

60220

2u.

35^

cnk

·<;e

6 0

2

50

25.

RF 7t„:t?s·

602U0

26,

60250

?;

<

<

= l;T I -'t r * LC FG ( , ' <. v A I..

r

m

ii &

o 5

70010 ?» ₇₀₀₁₅ ^ . ₇₀₀₂₀

'1.

r ₇₀₀₃₀ 700U0

c

70050 70060 * . ₇₀₀₇₀ 0. ₇₀₀₈₀ 1 .*>. v A L r H T R H S ( U ) ₇₀₀₉₀ 1 1 • Tsi , \ _7HJ0O 1?. «•( T ) - . i f i unvi. _{701 10} 70120

1<J, ^KAO( I ( VAL

)

.VA.L } • r > L 70130

IS. 7n "(T)ri... CT )-r>:t'l. 70100

1 b. P p T 1 I R \ ₇₀₁₅₀

-

37?-

S>01(

\,

s

Ijc

PL jV t _orkt_L

(-v,

#c , , s c

U,

Ac c,^ XF'11 v·

IPWT»

,* )

pooio

?.

I'^ucn

REA!_*8(

A-H,P«7)

,

1 VTEGF3*'J

(3-

eoci5

3,

_P0020

u,

C

P0030

5.

C «'

_{cL"i*T«A\ Suii^HUT}

_.

_r-R

_{, ^}

_{3A \-F?)} »· _T"»

_T^J?ATTOv

_ftOOao

6. c

PO05C

7,

c

^t^1;

J"

T'vG cj^ST

·*> :3

VAT] vf; S r> Tr·? UP

JFCTIVF

F! ._cTTf> 1 ' _enoAo

R, c

60070

Q,

c RV

_v,

_J,

_{, p^^lu}

_{4 «}

_pxe^gy

*esf

6°

f s ^_{t_} s *f fe^gi

and)

f

OOFO

in.

c

A0090

11 . eninn

1?.

PN./R/M1yf

13.

nT^^STC'?··

( 1 ₎ ,Gf 1 ) , -

(

u

P0120

1 'J. r

_{T*F_}

_VFXT

_Sfc"

_vF

₁

_NTFGf^S

_»A»TTTlfVJ

_{IrF ARSav} .·; _f j

30

IS, 0~_{= *} 801 «0

If.

I-r1r>n

_/£

_P01

₅₀

17,

*.s + *^ _*0160

1*.

TGAsTJTA*»'

801 70

19,

I «

1

, ₄

-P01

FO

2«.

-Qr_JAi _AO

₁

₉₀

21

. ;·.c=

I

r l>4S'

_{8 2 0}

Q ^I A Ci. ?Oc 1 0

23,

C

_en??

2'J.

C

^ M

Tj

L]^7

^0^30

25,

c

_P02tiO

26.

\ -

-v-iyRb

R -F V A<*"J

F_

S

_{P«2 SO}

2'.

0260

2P.

c

-

peQRlf> VARIA^LFS

8027

29,

0

₂

0

30,

F - f.K

jrc

1

vE

.' ,

vftlnF

pn^Qo

31

,

300

3?.

G - F RS rj R U V F F t?

0310

33.

C

0320

3u,

c

SH'P

-

IMTTAL OfAGF

I

VARJ ArlhS

_Rn

J30

3S.

603<

3<*.

C

Arc

.

(; \ µ

9(;Fr,CF

PA*A»«FTFP

PO3S0

37.

c

0

₃₆₀

5*.

r µ_{A /}FI!*'· rn vAy

IV!'M

Mj^bFR pF

FU^CTI0*··

b'VALUA

V _"S

P0370

30.

C

R03P0

tiO.

C ai

i.fvFo

^FFPRF

DEFAULT

pn

390

01 , C 80ti00

<i?.

C

TPP^

t «

I'.Tfc^vl.OT

ATI-

PP1WT0UT CU^TPOl

*_{f ^}

_s

_{Nf, pr r j 1}

ti3,

P.06

20

UQ,

c

ci Nf; ARRAY

DT^F

KS

J.PNJ 2'v**2

4 6fv r At |.

I*G PROGRAM

30

«5.

/I#. c

_POtifO

« | <17,

c

SFT

RP^F c

C'N^ S 0

5

0 80tiAO

tiR,

ACr.TzACC*6CC

P0ti7n

ti9,

_J

1 *

₎

R »

_P0ti80

50,

c

GIVE

_rJjTjAu

VAijifS

sn^F

VA»IAHLFS

P0ti90

51

,

DSSsSTEP*STKP

posoo

52,

a y =

1

_«0510

53.

TSPF>;C

=

₁

_POS20

54,

IPTFST^I

PO530

55,

c

CALCHLMF

TmF

IMTIAL

GRAOU^T

_P05ti0

56,

CI

Cilt

CAVCf-G(K

,

y,F,G)

«0550

QACL· 3 f § ROt>n0

5*,

c

₈₀₅₇₀

50,

c HSF

"US

Fnr^·

_J

SH $MR r Iit J F _C A

_1.CFG

₀

₅

₀

60,

c

P0S90

61 ,

c

c

A|_CFG

S GF Thfc

FOflv

B0600

6 ? . C s " a P f j' . « TrA L C F G( * .X . F.G ^ ^9--60610 C s " a P f j' . « TrA L C F G( * .X . F.G ^ ^9--r 60630 r P06O0 6 * • C eo65o *7. C * * * * * 60660

f>6, r CTvi r ' H I H VtU'TS TP 1UF C P ^ O E M S UF GG • - A\f> no 60670

b0. KST-SO. 80680 70. 60690 71 . r:sr' = GSr- + G( J > * «? 60700 7?. U f GS'.-IS.S* 2 60710 7?. ? cr,r>] = «'• 1 ons^t IGSC)/STfc* 507?0 7<J, »-r>7 fifXsi , / GGOI AG 60750 7S, rf = 80700 7*-. 60750 77. ^•i « T =1 , ' 60760 7P. ,1=1 80770 7*5. *0 7*0 80. 1 n n ^ - < p i> • 1 80790 8 1 . ₆₀₈₀₀ 8>. 60810 en 1 n i p i A08?0 K - < 4 1 80830 MS. AH6<J0 u (K ) r G G f") I A G 80850 «7. R0860 HP, 60670 60680 T «• f J - ' 1 j n J . 1 o(j. «J «0«90 91 . 1 rtfc AOQ00 9?. K ' tM">s K r» ft 4 y 80910 9^. - ( K i r n , 80920 9'... w(T H + O s 0 , 8O950 ~f<LfO=0. 609^0 r.r i r A 80950 97. 'j 80960

c A«>PA»T.F FOp A * v PKJf-.'T jKif* i n P E G I * 0 " A PASF 80970

60960

loo. 6 DIMM 7 80990

10 1. 7 COPt. M M ^1 # SV , M*-fe F H..LP* J *-:G n • i T P i' T T$ HF'iv J r>f »* V pPrFL «) 61 000

in?. r. o in 10 ₈₁₀₁₀ 1<v<. c n.J-.r,]!., A \ JTFPATJP^, UY TF_STT>G Ff.lQ C( VE Gt * C F 81020 lOtf , q GS^sO, 81030 1 ns, nn 9 Tzi,'- 61 0*10 1 06. 0 r-SR = GSrJ4G( 1 ) **2 81050 1 07, 1 A T F ' G S < - A C C 1 1 i 1 # 11 » 1 * 6.1060 1 0 A , c PPJVT T^T f- 1 Al_ v'ALl'KS N F Fjj*-CT)nf- 4^0 G ' A ^ I ^1 , T 61 070 5 oo. 11 TF f TP?) 17,17, J 2 81 060 lift. 1 ? 81090 111. 1 5 r M i ? M M ( / s x » u n t « M « , ' CALLS np- CHCFG. T^t. FT>AL F =S ft) 81 100 11?. r>« ji\,T i u, ( X{ l ) » l s i , ' 0 _BU10 1 1 <• 1 'i (SVf 1 > *S (6Kj HI 120 1 1'J. IF flPKT^T) 1 7, 17,1b 81 no 11«5. 1 5 PM1M 1 ^ , (G(T)#Jri,*0 M H O 116, 1 6 FHCvA T Cb^f ' G = ' , <6F)/J,A) 1 81150 117. 1 7 PFT L A ­ _{61 160}

l l « , r TEST ^FTHfp A XF I • NJ CALLS OF C A LC F G PAVF BFFv *Al>E 61 170

H * . 1 A TF (N A xf>"AXFl.rv)21 f 19, )Q 81 180 12*5 1 9 81190 1?1 . 2* Fi!?"A T (/«$*# 1 P'»*t L i , | / : k 9 ^ A ^ F ^ I b * ' CAl.t.S OF C A1 F F" G ' ) 61200 1??. r,n m 1 j 61210 1?3. c PBTs-T THF BtST VAIJ.lf. QF F t T f* 61220 12«. 21 TPTFSTsJPlFST»HHS(lP»TM) 81210 ias. TFf lPU'ST)??,??,i?S 61 240

1 2 * . ?? IPUSTsJPP 81250

1 •

P R I M \U, ( X ( T) , 1 = 1 , N ) I r. n a T A L'N •, 5 , i u X , ' " 1 , M u t o J ^-377-m/38 1 2 9 0

130. Tr UeRH'T)25.25,2u 81290

131 . ?u »RJ\T 16'.(GCT)«l = lfN;^ 81300

1 3 ? , C TEST AHET^ER A SPECIAL ITEPATIHN IS WEEDED, A'.O CALCULATE 81310

133. C THE CHANGE 1^ GKAQIEN'T ALO^G THE DIRECT 10 * OF 81320 134, c A SPECIAL ITERATION 81330 135. 25 ITSPECsITSPEC-1 81340 136, !F(ITS?EC)26.32#32 81350 137. ?6 DGGD=O. 81360 138, SGDD=O. 81370 13o, KDDsTOD 81380 u o , 00 ?8 I: ! , N 61390 141 . SUk' = 0 , 81400 142. KsT 81«10 143. K0=1 DO ' 61420 1 aa, J=t 81430 145. 1 05 JMJ-IHO6»l*7,l07 81 UUQ 146. 1 0 6 K0=KO+1 81450 147. SU-V = SUM + W (K ) * >s ( K D ) 81460 1 u.a, 81470 14Q, J = J+1 _{ft 1 4 8 0} 150. GH in 105 8 1 49Q 151 . 1 07 np 27 J = I ^ 81500 15?. KD=KD+I 81510 153. SiJMrSUV + w (K) *w(KO) 81520 15u, 27 X = K+ 1 81530 155. KDO=«DD*1 8 1 540 1S6. SGOO = SGDO*G( T)*w(«<nD) 81550 157. 2C OGGOsOGGntS'MMSu'-' 81560

158. c CALCULATE TWP CORRECTION FOR A SF EC I AL ITERATI'V, 81570 159, c AMD REVISE THE ARRAY DO 81580 160, OS') = DM I M 1 ( DSS # GSO/OGGO ) 81590 16 1 , C-^SIGN(OSQRT (OSO),-SGOO) 81 600 16?. 00 29 1 = 1 , - 81610 163, ••««' ( 1 + I A ) s C * ••• f I • I 0 0 ) 81620 160 , 29 w( IfIxR)rw( J+IDD) 81630 165. KOn=IOO ₈₁₆₄₀ 166, 00 30 ! s? , N ' 81650 167 . 00' 30 Js 1 , M 81 660 168 , KDOSK0041 81670 169, 30 ₈₁₆₈₀ 170, no 31 1 = 1f N 81690 171 • KODsKOOf1 81700 17?, 31 81710 173, TTSPEC=2' 61720 17/1, GO TO 51 81730

175, c CALCULATE THE GENERALIZED N-'E*" JTON CORRECTION TO X 81740 176, c AND PREDICT THE CURVATURE OF F ALUNG THE GRADIENT 81 750

177, 32 GGGG=0. 81760 178. 00 34 Js 1 # M 81770 179, / (T 4 I A A ) = 0 . 81 780 18o, SUv=0. 81790 181 . J=1 61800 182. K = I 81810 183, 1 OA IF fJ-I)109,110,110 81820 18*1, 109 C I -f I r« A ) = X ( J -f J W A ) • W ( J H • K ) * G ( J ) 81830 185. 'St.iMzSu* + w ( K ) * G ( J ) 81840 186, < = K 4 M - J 81850 187. JsJ+1 81860 188. GO TO 108 81870 189. 110 00 33 J s l 81880 190. W ( I 4 I XA ) s* ( I 4- I v«A ) «w ( THf K ) *G ( J ) 81690 191 . SiWsSUM*W('K ) *G( J) 81900 192. 33 K = K • I 81910 1Q3. 34 GGGGsGGGGtSuv*G(I) 61 920

194,

""

C

""

TEST

WHETHER

TO

SET

THE

CORRECTION

TO A

MULTTPLE

OF"

"

j>-THF

GRADIENT

^

195,

c

19f>.

TP

CGr,Gn*n&BSf

_{(;G(;G)*DSS»GSf;**3)35,35,37}

197.

c SFT

T*E

CORRECTION

VECTOR

A

*Ul.TlPLE

_{OF THfc}

_GRADIENT

198,

35

Cc-OSQ^T (DSS/GSiO)

1

_99,

On _3*

_1=1,N

200,

3

w(7tT>;A)sC*G(n

20

1 ,

GO

202.

c

SET

THF

_OPTIMAL

_STEEPEST

_DESCENT

_CORRECTION

_J»··

_*B

20?,

c AK-i^ THE

DIFFFRENCE

BETWEEN

'aA AND

IW

*C

20'J,

37

Cs-GSQ/GGGG

205,

C4=

_nt

206.

CR=

_0,

207.

OO

38

T=!,

20 P.

w(T+Tw8)sC*G(I)

20°.

(

+ '··

C

)=*

(

4

I

WA

)

-w

_(I

_4I

_aR)

2to.

rc i;'_{( }}

I

tvR

)

*···,

₍

₊

_J

w_f;)

2

J 1 e 3 Cfi=C"<+'-'(

T4l,

C)**2

212.

c

INTERPOLATE

FUR

_{THE CORRECTION}

_VECTOR

_{THE LIVE}

A - WR

2 ,

=D

$ $

-C*C*G SC'

2]/J,

c

FOLLOW I

r^'G

THRfrE CARDS ARE NQT

Pfn-'EL

' _S

215,

P('f'zC

* CA4C+

CB

2i

_fr. TP

_(Oi.^.LT

_.0,

)

_OMMsO.

217.

thf A=

OS

G-K-_(C/

(DA

HS ( _a

_{) 4DSQRT}

_{( OUM}

))

,

(:

A )

2l

A,

c

TEST

v.

HER

TO USE

_THF

GENERALIZED

ME^TON1

_CnRRECTIO*

219.

IF(

! »1

,)

39,41

, til

220

,

3q

on

1= ,

221

. U0 ( 74 I

)

=is

(

I4

I

-t8

)

4 _{F A}*V,

_{( I}

* c

)

222.

c: XD R S S

THE

CORRECT

J

DM

_{VECTOR I}

_TERMS

_(IF

THC

_{R{.I-S (IF DD}

223.

1

224,

> = D

225,

nn _ti?

I

1

_,^

226.

·8^

=

5 > ( I

4 V'A

_{) **?}

227.

V(HTV.R)=04

228.

Wf

_l4l;..C)=i),

229,

up

J;1 ,

23 ,

0 = )041

231

. u? '-

(

41

.µ)

=w

(

>

wb)

4w

( )

*w

( wA4j)

232.

c

REVISE THt

DIRECTIONS

IN

Mfc

ARRAY DO

233.

S=

n,

231,

KKZX

235,

43 F f·.«. f 4 I

₎

₎ti

5

,44 ,4S

23^.

Utl r ·1

237,

GO

TO

43

23

A,

/iS KKsKK-1

239.

P f <

₎

a

_8,

46 ,/J6

240

, 4A. 5SS4'·: (

I

-

)

**2

211

.

CrOSORT(S*(S4A(1XP4KK)**?))

2"2.

CA=S/C

213.

CB=

*(KK4lMJ)/C

24

4,

KOOsJDOf

N»*KK

215.

on _u?

2i*>,

xnnsKnoti

247

, >·( J4 1*-c )rA

(J

4

11-

C ) -f ·/( w 4 4t 1 *W

( [)0

)

218,

47 w₍

_on)

_=C

A*.·.

(

DO-

--J) »c e

_Aw

(,)

_wC

₎

219.

GO

4₅

250

, aft Kf)0=I00

251

. r>0 HI

Tr2,

rx!

252.

On 40 _{J t}

_,

253.

nr. ) >

251.

>·

₍

_{no )}Sis

₍

Op

4

N)

255,

Cr 1

,/f)SQRT

(osw)

256.

00

50

=₁ .

257

, = ^ >

25*.

50

(Knn)=c*i-(

J

41

·a

₎

259.

c

APPLY THE

CijPRECTIOM

VECTOR,

AND

CALCULATE

THF

317-

930

81910

81950

81960

81970

81980

8

990

82000

82010

82020

82030

820*10

82050

82060

82070

82080

82090

82100

82110

82120

82130

82110

82150

82160

82170

82180

82190

82200

82210

82220

82230

8$210

82250

82260

82270

82280

82290

82300

82310

82320

82330

82310

82350

82360

82370

82380

82390

82100

82110

82120

82130

82410

82150

82160

82170

82180

82190

82500

82510

82520

82530

82510

82550

82560

82570

R?58n

*60.

2611 .

c

51

UHJtCTlVE fUNX TI UN -/ C

82590

82600

262.

52

* ci*ixA)=x c n • * ci • I K A )

82610

263.

S'AyC = ^AVC*l

82620

260,

c

'vHTE

THAT Trip

MF*T J ^

s

T RlJC TI ON IS

'QT STANDARD FORTRAN! N

82630

265.

CALL CALCFG(Nj,f

.

:

tixAtn

.FA,w(iGA + n)

82640

266"".

" c

SET THF ERROR OF THE PREDICTED GRADIENT IN WR

₈₂₆₅₀

267.

c

ALSO CALCULATE SO*E NUMBERS FOR RfVlsiK-G THE STEP-BO'.'^D

82660

268,

DG = 0,

82670

26Q.

'HGArft .

82680

270.

DGGOsO,

826^0

271 .

•vRSCsO,

82700

272.

DO

54 1 = 1,*

82710

273.

SU*=0.

82720

27^,

<=I

₈₂₇₃₀

275."

J=1

82730

276.

1 1 1

IP(J-I)11?il13,113

82750

277.

1 1 2

82760

278,

' K s K + ^ - J

₈₂₇₇₀

27Q,

J = J+ 1

62780

260,

GO TO

1 \ 1

82790

261 .

1 13

DO 53 J= I » *

₈₂₈₀₀

282.

Su^-s SL'

w

't'*(•<)**( J* I *A}

8281 0

263.

53

"(S^*

1

82820

28 a.

>

: ( T • T ) r w ( I + I G

A

) -G (

T

j -S'l^

82830

255.

DG = 0r.*G( I )*>fI + I

'sA)

82840

286.

nGA = OGA + w(J*lGA)*fc(I*iw-A)

82850

287,

D

G

G

D = 0

G G

D + S U

A M

(I + 1

WA

j

82660

288 ,

5o

*• R

s S = *

R S

0 • '* (

I

•

I

* 3 ) * * 2

82870

269,

c

TEST

<*EThER 10

DECREASE THE STE^-BOUND

₈₂₈₈₀

290,

IF(ITSPEC*2)55

.bO

,60

82890

291,

55 IF (FA-F-n.1*DG-0,05*nQGD^57

,57

,56

82900

292,

56 OSS=fi,25*DSQ

82910

293,

GO

Tn 6 0

K2920

294.

c

TEST ».WETM£R TO INCREASE THE- STF.R-HQl.JND

82930

295,

57

OSS=DSR

₈₂₉₄₀

296.

IF f.vSSfv1»0»25*GSQ)59,59,58

62950

297.

IF(DG-DGA-DGA)60r59,5R

82960

29A,

59 DSS = 4.*0S0

82970

299,

c

SeT'T^E DIFFERENCE BETWFE'J G^ADIFNTS

82980

300,

6^ DQ 61 l s i . N

82990

301 .

6 1 •A( I + U C ) = *U*1GA)-G( T )

83000

302.

c

SET y, F AND G TO THF BEST CALCULATED VALUES

_{8301 0}

303.

IT^ETASI

₆₃₀₂₀

30 a.

IF (F-FA)64

P

64,62

83030

305,

62 c =

FA

_830^0

306.

DO

63 Tr 1 , s;

83050

307 ,

X ( I

) = v. (

I

• I

X A )

83060

308,

63

G ( I ) S W C H I G A )

₈₃₀₇₀

309,

c

CAICOLATF SOWE VFCTQRS ANQ SCALAR PRODUCTS TO

63080

310,

c

REVISE GG A\»o M

₈₃₀₉₀

311 .

6/i

SD** = 0,

83100

312.

GHD=0,

83110

313.

SEGsO,

83120

314.

DHDSO,

₈₃₁₃₀

315.

DO

66 1=1

83140

316.

to(T*TXA)s*W(ItIwA)

83150

317.

* ( I

• IG A)s 0,

83160

318.

Ks

I H

+I

83170

319.

J=1

83180

320.

1 1

a

IF(J-I)115M16,116

83190

321.

1 15

w ( I •

I

X A ) s W (I • I X

A

)

•

>

'

/

•

' ( K ) * A- ( J • I wc )

83200

322.

'* ( I

• I G A ) s (I

4

IG A ) • w (

K

) *

s

« ( J • I

W

A )

83210

323,

w = k • v - J

63220

324 .

J = ,H 1

83230

325.

GO TO

] I

IX

83240

1

lb

•.-

,

(I + JXA)s

,

A'(l4lXA)*W(K)*wtJ*IwC)

53db0

327.

•.-

,

(I + JXA)s

,

A'(l4lXA)*W(K)*wtJ*IwC)

83260

32*.

:A»(T4JGA)S> (I

+ I G A ) +w(K)**(J+IWA)

8327Q

329.

65 < s X 4 1 "

83280

330.

S0wsSD*+fc(I*IWA)*H(I+IWB)

83290

331 .

RHHSGHO+WCI+!*C)*"(l4lGA) 63300

332.

SEG = SEG4U)(I

+

T*C)*W(l4lXA)

83310

333.

66 DHO = DHD + k( I f!>A)*K(l4lGA)

83320

334.

C

TEST WHETHER THE USUAL CORRECTION TQ GG GIVES

83330

335.

C V£AR

SINGULARITY

833U0

33^.

HHT v = SFG*0

H

f)-GHD*GHO

83350

337,

pn TO (67,70),I

THETA ₈₃₃₆₀

33«.

67 TF(DABS(HDlv)-0,1*DSD*DSQ)66,7 0,70

₈₃₃₇₀

339.

C

CHANGE THE D I F F E R E f

J

C F I N GRADIENTS TO AVOID SINGULARITY

83380

340.

68

CASHDIV/(0SC*D5O)*0,1 83390

341 ,

CR = GHD/DS

(J

-'0 .1

83400

34?.

C

THE FOLLO^l^G THREE CARDS ARE *0T PQ*El'S

83410

343.

D'i

"'Si. 9*CA + CR*CB

83420

344 ,

IF (DU".LT,0.) "DUMSO," _83430"

345.

CArCA / ( CA*CB*OSIGNi(()SQRT (OUi*.) , CA + C8))

63440

346.

CF> = ( 1 ,-CA) *SDfVDSg

83450

347,

00

60

1 = 1 ,

K' 83460"

3 tJ A ,

C = C A *

( C

R *

{

I * 1 w A ) - w ( T 4

T

u B ) )

83470

34

Q . v (l4ii--B)sKi4lwB)4C 83480

350,

69 '>'(T*IrtC)s'w( J4IWC)4C

63490'

351.

ITHFTAS2

83500

352.

GO in 64

63510

353,

r

RE'vist THE *ATSilCES "GG AND H

83520

35".

70 CAsl ,/DSO

₆₃₅₃₀

355.

rprSD»'*C A *CA

83540

356.

CC=DHD/HD1V

₈₃₅₅₀

357.

CDrGHP/HDIV

₈₃₅₆₀

35*.

CE=SFG/HDIV

83570

350.

83580

3*o .

r^O

7 1 T = 1 , N

83590

361 ,

on 71. J = T,N

83600

362.

K = K41

83610

363.

W ( K ) 2

*• ( K )

4

C

t * ( W (

I

4

I

W

A ) *

W ( J 4

I

W

B

) 4 W ( J 4

T

W

A ) *

83620 W ( J

4 J

IV

6 ) )

3b /•,

t-C^*

;

V(l4lwA)*W(j4lWA)

83630

365.

71

.< ( K • T

H

)

=

W (

K

4

T

H )

-CC * w

(1 4

I X A

)

*

W ( J4

I X A J - CE *

w (

I 4 T

8364 0 G

A ) *

h ( J

4 I G A j

36^ ,

\* C D * f

!• ( I

4 I X

A

) *

U (

J

4

I

G A

) 4

'A' (

J • I X A ) * W

( i

t T G A ) )

83650

367.

GO m « 83660

368.

E NO

83670

377-

""J

Sii^rtf'UT J NE D RSER_{( ,}r_{,X ,}* _{, S} ,DEL ,

9HC

)

90010

'IV.0LICIT

REAL*6(A-H,0-Z)fIMEGER*ti(l-N)

C******«************************************************* C C

""MRECT"SEARC^·

SOL.MTin-j

OF '

NUMERICAL

AND

Statistical

PROBLEMS"

C 3V

KO«FRT

HQCKE

AND

_T,

_A,

_JFFVES,

JAC*I

VOL

8 *0

2

(JI'LY

1962),

c

c

* -

H'MdER

OF

VARIABLES

c

f

_Function

minimized

and

*ust rf

declared

external

c

1

\

_THE

· ·A

_I

_PROQRA*

c t "

» ThF VAR

J

ABl.ES

C f&x -

Maximum NUm»*ER

Op

xpLOR

A HR

SEARCH

TO

BE

ALLOWED

C

EPS

-

SIZE

that

DEL

Can

*£

c

del

-

amount to re added

variables initially

c Rµ0 - A

NUMBER

BET*Ef*

0 and 1

USED

TO

REDUCE

DEL

C

c*********************************************************************

DIMENSION)

X

_{(1) #PHJ}

_(ti5),

_TM^TA

_f

_ti5)

C

<

_-ILL

HF

USED

TO

_KEEP

_COUNT

OF

T*E

_{EXPLORATORY SEARCHES}

=

C

BEGlr ThE

DIRECT SEARCm PROCEDURE

C

COMPUTE THE FUNCTION

AT

THE

PRESENT

RASE

SsF(x)'

c

RfcGjN

TmE

ExPLORAIORv

SEARCH

1 nO

? 1=1,

PHTU)

=

-X(I)

? COM

Sl=S

< sk 11

C

HAVE

>'E

^AxjMUM

I'"

_f

OF

EXPLORATORY

^nvES

' *

*·'

_*ADE?

F

_(K.LE.fAy)

GO

TO

3

C

TUF

_{· ^ NUMBER}

_OF

_EXPLORATORY

_{KqvES have BEEN}

_"ADE

*R

(

1 OB

#11)

MAX

RE

TURN

c

thf

_{may m ^}

DUMBER

of

exploratory

^oves have

*·

_{pee* ^ade}

r

_{Rfr, V·:}

_A,N

_EXPLORATORY

_'*OvF

3 nO 5

1=1,N

P«T(I)5PHI(1)*0EL

PQprPUl

=F

(Phi

)

IF

(F0FPHI.LT.S1)

GO

TO ti

v-1

(T)rPMj

(1)

-

?.

*

L

FOFP^IrF(PH

j)

IF

(F0FPmi.LT.S1)

GO

TO

a

PHI(I)=PHI(I)*DEL

GQ

TO

5

U

_S!=FOFPHI

CO^timie

c

FhD of

exploratory search

IY

(SI.LT.S)

GO

TO 7

C

IS THE

STEP SI7E SMALL ENOUGH?

JF

(OEL.LT.EPS)

GO TO

6

C

REDUCE

THE

STEP SIZE,

THFn

DO

AN

_EXPLORATORY

_SEARCH

OEL=RHn*r)EL

GO TO 1

C

THE

STEP

SIZE

IS

S''-AI.L

ENOUGH FOR

CONVERGENCE

h

WRTTF

(106#12)

RETURN

C

R

_GI

PATTERN

_M(,VES

7 Do

ß 1=1,

F

A

₍₁

₎

=>:

(I

)

y(i)sPHHi)

6?#

s=s1

_j77„

_/»/<?

₉₀₆₂₀

6?,

ß continue

90630

fcti„ do 9

_i=!,^

₉₀₆₄₀

6s,

p"t

(1)=2,'* 1

( )- ( )

" "

"90650

6*.

ch^ttmjf.

₉₀₆₆₀

67.

cnfphi=f(phj)

₉₀₆₇₀

t>a. if

(fqfphi

,tt«

si)

go to 10

" ~ "

90680

6c.

c move was a

failure.

go to

exploratory

search

90690

70,

go . 1

₉₀₇₀₀

71 ,

0" si

=fnfphi

" " " " """

"90710

7?,

c move w»s a

_success,

_«

_another

*ove

_{i* the ra*e}

_direction

₉₀₇₂₀

73.

go to 7

₉₀₇₃₀

7^,

11 fophat

_{ciho,75,'exploratory}

searchs

have

been

made/

with nq

conve

9074b

75.

*rgencf')

90750

7ß.

1?

format

_{('ocqnvergence}

has been

reached*)

90760

77.

"

-^--377-

?/9

Si,uprL:

N-tf

L

iC^xSiM.K.

A,

?

_.fr,,FL.

· &.

1

T**CF

.

CE'»·

*11, ,

PI

,

TPRNT)

Tm&LJCTT F:tf

Al

*6 (

- ,

n-7)

·

1

*·-·_{F S * ( 1}

₅

, 1

s )

, ( :

)

, «I

(

)

;

_

(

X1)

.

I

C

3

^ .

I

C ( ) # D

c

^

)

ni^FNSlO\!

_{Ai(i5,i5),F(3«sl,:?(15flS),rnS).XClS)#}

_{DFL ( 1 5 )}

. ?M

1 5

, l fa ] AV_s

_DCS

*F

_vftTPjy

00

1

]5J

^P 1

0=

1 , · f

J, I

)= (

1

, 1 _c

₀

> \·_i}

C^EC*

\·

_POSSIBLE"

TP

_ACE"

F

_{j_}

_S

rv.

_S

_!:1

7s _{c (}

_I

₎ =

I*·'

(7( )

.L7,CUV~IM

7C

_)=0,0

:

IT*ACF(T)=1

Sn Crv-

T 7

_MJE

r

(

J

)

HO &copy;

J

= ₁ . * -

()

=C . 6

is)

' c =

m

j) * * _{c . j} ) * _c

_j)

A

c

\: ₇ s.

_*1F

sIi'· _Y 10 1 Yp ß «?s

_.

· · 2 I r₁ , h 7 ( , F ^ .

I ' F

( ) ) , I . ^. Hk

(

) , ) ,

J

.

F.(y

,

I

; ·

t\

f ^ ) )

Gp

TP.

2

7F ( 7^?

CE

C ) ,

·

.

)

;

yha»SYRA»*z f )

?

Cf' _{! *}'_! F 7 * _{I F r}

₎

₃

₁ = ₅ , '·· f ₍ 70

C .

. 0 ) . 7 .

5)

( )=?(] )

*

_?·*!'(

_J

)

*·" c

_tF0.

^ '

1)

.0».*!

_{,F.r:',IP!!PF(P)}

, ,

.EU.

IP.»Pc

C3)

)

GO

₃

ni=?fI)*FLC7)/Y^A(v

JF

(G1

_.LF.O.

)

GO

TO

₃

* _{C ) sP f}

_I

_{) f C I}

_)*OLUG

₍

_{r,j )}

₃

5

1 f _{( 7}

₎

= _{. c}

3

C

'

_y

\11_e FT

F

·_If'

_'

_UF

_THE"

_(.

J,

) r- 1

I

!

5

J=

₁

, "

₅

<r

J

, ·

(

J , ) = . ^ ; U

₁

=

1

# * F

(

7PACE(I

)

_{, . )}

GO

(J,) *(J

* <

)

+* (

I

,J)*

7

(J

_{, )} *

/

(

^ 7

'·!

7F

R(*

,

J)=P(.J,*)

S '· JMiF

D

F

F

_I

_F

_LAST

_Qtj,, f-j₀ ( F R

(

ijn

I-G^

^_{7 0 ?}

, 7

J

= _{1 ,}

(

J , ^ 1

)

s

( J

)

(

< ,

J

)

( J )

7 cn?v 7

₇

IF

(

1

, *1

)5

ß ) 7 F y ;_(.

_|JGMF

7 F

_l>

_COLU"*

₍

_{J ,} "

_?

^

1 = 4 ₎ no ß

J=1,f

(.J

,

)

s .

_J

r

₁

, TF-

(

7

RACE

c I ) ,

'vK

e

)

r;p 7 r

P(.J,f*P)=P(J,M*2)*A7n,J)*F(T)

t?,

crr.'TT.NUE

63

„ C

DFTERV-T

µ

FCV)

arvD

R("-m,m

+;>) b'J,

PrtFv-fi,

377-

" 2

6S· - 1=1, *··

66,

F

(

npACF

(

.rit

.01 67. FPiP Y=FnFv_{+ r I )}

6«f

CO- TMJE

69. vpp=y>?

?n

„

R(*Pi

,^P2)=FPFv

71.

C

SnL

VF_ THE

SvSTt*

Ff.R

_PHI)

A^O U

(STORED

IN

PI(v.«H)i

7?.

[ML STr

F&^(

,^P?,P,PJ

, D ,C# IS. 56}

73 ,

usPj

f

'· ))

7/4,

c

Cfu"D,JTE

*BAR '

XI)

7^

.

X"AR=YFAR*(Vt1

, ) 76. DO 11 1=1 , Ni 77. IF (

JTWACf-t

J 5 ,

*E,0)

, -

53

78.

Si'-'so,

7 ·

*r. _{50 J=1}

60,

SU^=Si,M+

_^I

U)

_{*U c}

_I,

_J) 61. 1 COvT NI.'E

ß?.

*CT)=-F(J)+/fI)*X&AR/yRAR*SU^*7(T

)

B3

. GO 1 'J.

S 3

m

-(1.

0

65.

1 1 COr> H'lfc

66.

C

CH^PUTF

DFLCI)

87.

on

\?

1=1,N

6R.

^FLCT)=XC])-7(T)

6P.

F C

T5ACP

CI

)

.»,'t,

0 3

_f>FLCT)5C,0

90. \ ? Cf'M !

M'F-91,

C :µ_p.r F of<

_cn.WFPGF^CF

92,

OSQ=o,

93,

On \3 ici 9y, r>S^=

^SC+DF

L (

) **?

95.

13

Cn*TTNii£

6 , TF (

nsfJPT

( )

,LE

, 1D«fe} ofcTURN

97,

C PFU'u:v J RHP *··

'

IMI

7 FCRwtn

96,

CALL

1 (

_RHo,

DEL

. , AMI,,FI_ _, YBAR,

XBAR,

7# I

PURE

_, TRACE )

PP,

C FS v_{A F ^E'*} V

_{( )}

100,

1 ti 1= 1 ,N-'

101.

tf c

^ ct

( ),Ni ,

)

r, \u 1 ₀₂, 7

(

) =7( +

RHn*f3EL

( I )

103,

1 CnvriMit

10 ,

IF (

TPRN.T.EQ,

1)

WRJTE

( 1 ^. 1

5

)

(

7(

I

) . 1= 1 ,

)

.

('

7= ·»

(71·

_15.65)

106,

c

DFTFRMJKE

IF

*

_{Yd) LESS}

THAW

_COmmIN,

AMD

IF

SO

CALL

IT

107.

C

TRACE

ELEMENT

1 OR. r>n

_s?

T =_{l ,} 1OP , TF (7

(

)

.1

1

,r.n*f·

I;0 7(

I

)

=

0,

?

I

*AC

F

U )

=

1

Uo,

s?

ch^TI^'IF

ill,

no mi

11?,

end

-d--

377-

»?2'

1 . 5ij ?r. i HP

D,

.C# .5"^ ,

SU"*

, ,

I., 2

)

?.

tk-pu

tc

V

«Fai

*et

i- , - )

3.

ni^FASiu^

C(

)

,c

(

,P( . (

,L(i

j # it ( )

ti,

5!r;DrSU^v»Su^>

5.

=1

fe, C

cn^PiiTF

1WF LAMPT-ft

_pGSl

T1vfc

X·_S

7, 1 , *. no 1 i=i.* 9, IF

_{(0(1).GF.n,C)}

GO TO 1

1 ,

x'=-Y f ] )/^

(I

)

11,

IF

(f?^n.L

1 . yi

GO TO

1

i?,

=^=v

13.

1 C?"'· Tr.MF

1_ti, c

CO^c<-Tt: THE

DIcFCT10!-iL

OF^lVAilvfe

15,

2 St,v=

f)„n

16, *

= .

17,

r

_{( ( ^, )}

GO ₃

1»,

SI!V-S|?MTP

(7 )

+C

)

ic, TF (

_T,Ff:sL(

_,e.neL(r?)

_,CP.l

_,Fr;eL

f

_m

G<"

20,

ARG=f V (

J W«hp*D

CI))

/ f Sl,MY+

PHO*SU^D)

21,

ARG=APG*P(1)

2?,

TF

(ARG.LE

.0,0)

GO 3

2*.

Sl

-rS'-."*n

(I)

*Dl. L-G(

A«G)

?u,

3 cn'-'TTMf

25.

TF

fSi'^.l.E.O.O)

PfcTUPK

26.

RhPso

XP*R*U

27.

KFYPrKfyP+l

2R,

GO m ?

20,

F»jO

1 , 51:a . J \= , S1 mF(v\

(

U_{, \} } _{, , ,} fc f0_, ~

, * #'<1·*

CP1

)

?.

TvDt

1

st

_{.*8( »^, .·7)}

3,

^1 veK-ST0*: Af V3C

, \

RCPl )

»

Of^Pc

,

N^CPJ

)

, yc 1)

, c

1

< SVKF THAT \

ts

LESS

OP F.QII&L

TO

THE

9fc»

_{HF n-n.}

_S,

,

*·

_c,Lf,K.^ci

r.n *_» ·' Th rn >f< ·COV) R 7, QOt) ^ « ·" _:·

Rjr;e

»·.

" .

_hE

' ,

T5,

'

LESS,

ft_{, ·} « _{!r1 ,} e ijo C 3=

0.

10.

£9= .

1 1 . 3HI·QV 1 2. c 1v

7-* _

_S'J"F;

_CPVSTA^T^

1 <. 5R · '~·_{1 r}·µ-1 1 , 757 · '=0

15.

r

_rPfcATt"

_{T^F <·.·(.' * \Q}

16.

^ 5· _{Jc1 /} 17, • · 1 ° .

,,!)

= f

I

,. . .r.· _* '_;f

2*.

C

11<·

_GI

· _{ut v.}4 j n.\

_pf

_,f

_{f_}

_{m_'RF}

2i

. -

51

J=1

2^.

C 7»«F

_{> ^·}

f.·L'! ' ·1

V&L,!F

23.

7Vf 1 _,,

? .

5? , ,

-?s.

TF f

rv.^sf

)

_{eGT ,( *#<}

scr>(

,,!))

)

r,r.

TC.'

5?

2*.

]

vmrr)( I ,

J)

27,

2«.

S? ; · _11F

2»,

TF

('<;«·.·,"

_f:elu

Tf- _«j/

3^.

T' r r «.·, ,·

r;p * s

U

Pi'T '

J

,y''**

_C^'·

···'< V A1..11F fir. f)

I

- ^ .. 31 . 7 S fv = 5 '

32.

53

JCra=.i.'-P3

33.

r>ii'-'vV=nc

TrO,,

JCf.L

₎

3'J,

r^nur» ,

JCni)rD(J,

JCr<)

3S,

< _J, -1

CnL

1=Di·-

3A,

5

3 · J

»..«.f

37 , r r Ts" TF 61.!, F F''t: S RFLO'

^JAf-O'-Al

3A,

5/j

,1 _{3.1 1}

3°,

r· s-Li , fLf. =(

(

,

/·>(..r,.J)

0 5 _, r.r- _r;,

_K(;nL=J,'^l

U?. *r· ,^c.fv ) =r- ('. '-r

riu

)-rir *0 (j

,

)

^3.

S 1 c;iv 1 7,·

«J<J , r

CnrP-iTf-

VA^Ht

FM^

7u£

*· 7 F

k'·']

*jA'-!T

'JS, F

.K

21 _. Z*4%, f)«' 1 ; 1 ,fv ti7 , f t

Ff-s^fc

fe *n

(I,

I) R. ' 7 7'·'

'[·

Q, C 1 r T^r : < f'F fru-· h6r C_{F S »«F} PF _«

_{Luf. TMF. SI}

_{· r-F}

Sr.

C

F

!>F TFR"· \; ·7 51 . TF

(1 ? '/2*?, : ·

JSIf?'-)

DETERS-DET^R

5?.

C

cMffiK

Fi »v

S

f"Gi _A&

1

51.

tf

( · 8 Uf;TF

_/iT,ii><?)

_(;n

_{T(; b9}

5u.

r r f 1 #< <?8

)

5^.

•79* ,; '- 7

f1l0,«

6 U' _{JS S ^GH}

_L

_{fv I)}

5*>,

•V) 6^ I5

1Z·'

57,

>'r )S_0·

S«,

FTF s _, , Uµ j (ir .: 6_0.

C

HFC, C*<

_SUM

_ST

₁

ivT

ION

»1 . so y f ·)=,')r·'. ^P / r \

00010

S

>7~

DO S7

T s l • "

00630

006«C

X(K)sXf -0(<,J«-1 ) * X(J*

n

0065C

b7.

b * . ~ -

0067C

6>9.

57

0068C

QC69C

71 . ~

0070C