C DEL2 10
C ..................................................................DEL2 20
C DEL2 30
C SUBROUTINE DELI2 DEL2 40
C DEL2 50
C PURPOSE DEL2 60
C COMPUTES THE GENERALIZED ELLIPTIC INTEGRAL OF SECOND KIND DEL2 70
C DEL2 80
C USAGE DEL2 90
C CALL DELI2(R,X,CK,A,B) DEL2 100
C DEL2 110
C DESCRIPTION OF PARAMETERS DEL2 120
C R - RESULT VALUE IN DOUBLE PRECISION DEL2 130
C X - UPPER INTEGRATION BOUND (ARGUMENT OF ELLIPTIC DEL2 140
C INTEGRAL OF SECOND KIND) IN DOUBLE PRECISION DEL2 150
C CK - COMPLEMENTARY MODULUS IN DOUBLE PRECISION DEL2 160
C A - DOUBLE PRECISION CONSTANT TERM IN NUMERATOR DEL2 170
C B - DOUBLE PRECISION QUATRATIC TERM IN NUMERATOR DEL2 180
C DEL2 190
C REMARKS DEL2 200
C DOUBLE PRECISION MODULUS K = DSQRT(1.D0-CK*CK). DEL2 210
C SPECIAL CASES OF THE GENERALIZED ELLIPTIC INTEGRAL OF DEL2 220
C SECOND KIND ARE DEL2 230
C F(DATAN(X),K) OBTAINED WITH A=1.D0, B=1.D0 DEL2 240
C E(DATAN(X),K) OBTAINED WITH A=1.D0, B=CK*CK DEL2 250
C B(DATAN(X),K) OBTAINED WITH A=1.D0, B=0.D0 DEL2 260
C D(DATAN(X),K) OBTAINED WITH A=0.D0, B=1.D0. DEL2 270
C DEL2 280
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED DEL2 290
C NONE DEL2 300
C DEL2 310
C METHOD DEL2 320
C DEFINITION DEL2 330
C R=INTEGRAL((A+B*T*T)/(SQRT((1+T*T)*(1+(CK*T)**2))*(1+T*T)), DEL2 340
C SUMMED OVER T FROM 0 TO X). DEL2 350
C EQUIVALENT IS THE DEFINITION DEL2 360
C R=INTEGRAL((A+(B-A)*(SIN(T))**2)/SQRT(1-(K*SIN(T))**2), DEL2 370
C SUMMED OVER T FROM 0 TO ATAN(X)). DEL2 380
C EVALUATION DEL2 390
C LANDENS TRANSFORMATION IS USED FOR CALCULATION. DEL2 400
C REFERENCE DEL2 410
C R. BULIRSCH, NUMERICAL CALCULATION OF ELLIPTIC INTEGRALS ANDDEL2 420
C ELLIPTIC FUNCTIONS DEL2 430
C HANDBOOK SERIES OF SPECIAL FUNCTIONS DEL2 440
C NUMERISCHE MATHEMATIK VOL. 7, 1965, PP. 78-90. DEL2 450
C DEL2 460
C ..................................................................DEL2 470
C DEL2 480
SUBROUTINE DELI2(R,X,CK,A,B) DEL2 490
C DEL2 500
DOUBLE PRECISION R,X,A,B,AN,AA,ANG,AANG,PIM,PIMA,ARI,AARI DEL2 510
DOUBLE PRECISION GEO,SGEO,C,D,P,CK DEL2 520
C DEL2 530
C TEST ARGUMENT DEL2 540
C DEL2 550
IF(X)2,1,2 DEL2 560
1 R=0.D0 DEL2 570
RETURN DEL2 580
C DEL2 590
C TEST MODULUS DEL2 600
C DEL2 610
2 C=0.D0 DEL2 620
D=0.5D0 DEL2 630
IF(CK)7,3,7 DEL2 640
3 R=DSQRT(1.D0+X*X) DEL2 650
R=(A-B)*DABS(X)/R+B*DLOG(DABS(X)+R) DEL2 660
4 R=R+C*(A-B) DEL2 670
C DEL2 680
C TEST SIGN OF ARGUMENT DEL2 690
C DEL2 700
IF(X)5,6,6 DEL2 710
5 R=-R DEL2 720
6 RETURN DEL2 730
C DEL2 740
C INITIALIZATION DEL2 750
C DEL2 760
7 AN=(B+A)*0.5D0 DEL2 770
AA=A DEL2 780
R=B DEL2 790
ANG=DABS(1.D0/X) DEL2 800
PIM=0.D0 DEL2 810
ISI=0 DEL2 820
ARI=1.D0 DEL2 830
GEO=DABS(CK) DEL2 840
C DEL2 850
C LANDEN TRANSFORMATION DEL2 860
C DEL2 870
8 R=AA*GEO+R DEL2 880
SGEO=ARI*GEO DEL2 890
AA=AN DEL2 900
AARI=ARI DEL2 910
C DEL2 920
C ARITHMETIC MEAN DEL2 930
C DEL2 940
ARI=GEO+ARI DEL2 950
C DEL2 960
C SUM OF SINE VALUES DEL2 970
C DEL2 980
AN=(R/ARI+AA)*0.5D0 DEL2 990
AANG=DABS(ANG) DEL21000
ANG=-SGEO/ANG+ANG DEL21010
PIMA=PIM DEL21020
IF(ANG)10,9,11 DEL21030
C DEL21040
C REPLACE 0 BY SMALL VALUE DEL21050
C DEL21060
9 ANG=-1.D-17*AANG DEL21070
10 PIM=PIM+3.1415926535897932 DEL21080
ISI=ISI+1 DEL21090
11 AANG=ARI*ARI+ANG*ANG DEL21100
P=D/DSQRT(AANG) DEL21110
IF(ISI-4)13,12,12 DEL21120
12 ISI=ISI-4 DEL21130
13 IF(ISI-2)15,14,14 DEL21140
14 P=-P DEL21150
15 C=C+P DEL21160
D=D*(AARI-GEO)*0.5D0/ARI DEL21170
IF(DABS(AARI-GEO)-1.D-9*AARI)17,17,16 DEL21180
16 SGEO=DSQRT(SGEO) DEL21190
C DEL21200
C GEOMETRIC MEAN DEL21210
C DEL21220
GEO=SGEO+SGEO DEL21230
PIM=PIM+PIMA DEL21240
ISI=ISI+ISI DEL21250
GOTO 8 DEL21260
C DEL21270
C ACCURACY WAS SUFFICIENT DEL21280
C DEL21290
17 R=(DATAN(ARI/ANG)+PIM)*AN/ARI DEL21300
C=C+D*ANG/AANG DEL21310
GOTO 4 DEL21320
END DEL21330