C ELI1 10
C ..................................................................ELI1 20
C ELI1 30
C SUBROUTINE ELI1 ELI1 40
C ELI1 50
C PURPOSE ELI1 60
C COMPUTES THE ELLIPTIC INTEGRAL OF FIRST KIND ELI1 70
C ELI1 80
C USAGE ELI1 90
C CALL ELI1(RES,X,CK) ELI1 100
C ELI1 110
C DESCRIPTION OF PARAMETERS ELI1 120
C RES - RESULT VALUE ELI1 130
C X - UPPER INTEGRATION BOUND (ARGUMENT OF ELLIPTIC ELI1 140
C INTEGRAL OF FIRST KIND) ELI1 150
C CK - COMPLEMENTARY MODULUS ELI1 160
C ELI1 170
C REMARKS ELI1 180
C MODULUS K = SQRT(1.-CK*CK). ELI1 190
C ELI1 200
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED ELI1 210
C NONE ELI1 220
C ELI1 230
C METHOD ELI1 240
C DEFINITION ELI1 250
C RES=INTEGRAL(1/SQRT((1+T*T)*(1+(CK*T)**2)), SUMMED ELI1 260
C OVER T FROM 0 TO X). ELI1 270
C EQUIVALENT ARE THE DEFINITIONS ELI1 280
C RES=INTEGRAL(1/(COS(T)*SQRT(1+(CK*TAN(T))**2)), SUMMED ELI1 290
C OVER T FROM 0 TO ATAN(X)), ELI1 300
C RES=INTEGRAL(1/SQRT(1-(K*SIN(T))**2), SUMMED OVER ELI1 310
C T FROM 0 TO ATAN(X)). ELI1 320
C EVALUATION ELI1 330
C LANDENS TRANSFORMATION IS USED FOR CALCULATION. ELI1 340
C REFERENCE ELI1 350
C R. BULIRSCH, NUMERICAL CALCULATION OF ELLIPTIC INTEGRALS ANDELI1 360
C ELLIPTIC FUNCTIONS. ELI1 370
C HANDBOOK SERIES OF SPECIAL FUNCTIONS ELI1 380
C NUMERISCHE MATHEMATIK VOL. 7, 1965, PP. 78-90. ELI1 390
C ELI1 400
C ..................................................................ELI1 410
C ELI1 420
SUBROUTINE ELI1(RES,X,CK) ELI1 430
C ELI1 440
IF(X)2,1,2 ELI1 450
1 RES=0. ELI1 460
RETURN ELI1 470
2 IF(CK)4,3,4 ELI1 480
3 RES=ALOG(ABS(X)+SQRT(1.+X*X)) ELI1 490
GOTO 13 ELI1 500
4 ANGLE=ABS(1./X) ELI1 510
GEO=ABS(CK) ELI1 520
ARI=1. ELI1 530
PIM=0. ELI1 540
5 SQGEO=ARI*GEO ELI1 550
AARI=ARI ELI1 560
ARI=GEO+ARI ELI1 570
ANGLE=-SQGEO/ANGLE+ANGLE ELI1 580
SQGEO=SQRT(SQGEO) ELI1 590
IF(ANGLE)7,6,7 ELI1 600
C REPLACE 0 BY SMALL VALUE ELI1 610
6 ANGLE=SQGEO*1.E-8 ELI1 620
7 TEST=AARI*1.E-4 ELI1 630
IF(ABS(AARI-GEO)-TEST)10,10,8 ELI1 640
8 GEO=SQGEO+SQGEO ELI1 650
PIM=PIM+PIM ELI1 660
IF(ANGLE)9,5,5 ELI1 670
9 PIM=PIM+3.1415927 ELI1 680
GOTO 5 ELI1 690
10 IF(ANGLE)11,12,12 ELI1 700
11 PIM=PIM+3.1415927 ELI1 710
12 RES=(ATAN(ARI/ANGLE)+PIM)/ARI ELI1 720
13 IF(X)14,15,15 ELI1 730
14 RES=-RES ELI1 740
15 RETURN ELI1 750
END ELI1 760