C JELF 10
C ..................................................................JELF 20
C JELF 30
C SUBROUTINE JELF JELF 40
C JELF 50
C PURPOSE JELF 60
C COMPUTES THE THREE JACOBIAN ELLIPTIC FUNCTIONS SN, CN, DN. JELF 70
C JELF 80
C USAGE JELF 90
C CALL JELF(SN,CN,DN,X,SCK) JELF 100
C JELF 110
C DESCRIPTION OF PARAMETERS JELF 120
C SN - RESULT VALUE SN(X) JELF 130
C CN - RESULT VALUE CN(X) JELF 140
C DN - RESULT VALUE DN(X) JELF 150
C X - ARGUMENT OF JACOBIAN ELLIPTIC FUNCTIONS JELF 160
C SCK - SQUARE OF COMPLEMENTARY MODULUS JELF 170
C JELF 180
C REMARKS JELF 190
C NONE JELF 200
C JELF 210
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED JELF 220
C NONE JELF 230
C JELF 240
C METHOD JELF 250
C DEFINITION JELF 260
C X=INTEGRAL(1/SQRT((1-T*T)*(1-(K*T)**2)), SUMMED OVER JELF 270
C T FROM 0 TO SN), WHERE K=SQRT(1-SCK). JELF 280
C SN*SN + CN*CN = 1 JELF 290
C (K*SN)**2 + DN**2 = 1. JELF 300
C EVALUATION JELF 310
C CALCULATION IS DONE USING THE PROCESS OF THE ARITHMETIC JELF 320
C GEOMETRIC MEAN TOGETHER WITH GAUSS DESCENDING TRANSFORMATIONJELF 330
C BEFORE INVERSION OF THE INTEGRAL TAKES PLACE. JELF 340
C REFERENCE JELF 350
C R. BULIRSCH, NUMERICAL CALCULATION OF ELLIPTIC INTEGRALS ANDJELF 360
C ELLIPTIC FUNCTIOMS. JELF 370
C HANDBOOK SERIES OF SPECIAL FUNCTIONS JELF 380
C NUMERISCHE MATHEMATIK VOL. 7, 1965, PP. 78-90. JELF 390
C JELF 400
C ..................................................................JELF 410
C JELF 420
SUBROUTINE JELF(SN,CN,DN,X,SCK) JELF 430
C JELF 440
C JELF 450
DIMENSION ARI(12),GEO(12) JELF 460
C TEST MODULUS JELF 470
CM=SCK JELF 480
Y=X JELF 490
IF(SCK)3,1,4 JELF 500
1 D=EXP(X) JELF 510
A=1./D JELF 520
B=A+D JELF 530
CN=2./B JELF 540
DN=CN JELF 550
SN=TANH(X) JELF 560
C DEGENERATE CASE SCK=0 GIVES RESULTS JELF 570
C CN X = DN X = 1/COSH X JELF 580
C SN X = TANH X JELF 590
2 RETURN JELF 600
C JACOBIS MODULUS TRANSFORMATION JELF 610
3 D=1.-SCK JELF 620
CM=-SCK/D JELF 630
D=SQRT(D) JELF 640
Y=D*X JELF 650
4 A=1. JELF 660
DN=1. JELF 670
DO 6 I=1,12 JELF 680
L=I JELF 690
ARI(I)=A JELF 700
CM=SQRT(CM) JELF 710
GEO(I)=CM JELF 720
C=(A+CM)*.5 JELF 730
IF(ABS(A-CM)-1.E-4*A)7,7,5 JELF 740
5 CM=A*CM JELF 750
6 A=C JELF 760
C JELF 770
C START BACKWARD RECURSION JELF 780
7 Y=C*Y JELF 790
SN=SIN(Y) JELF 800
CN=COS(Y) JELF 810
IF(SN)8,13,8 JELF 820
8 A=CN/SN JELF 830
C=A*C JELF 840
DO 9 I=1,L JELF 850
K=L-I+1 JELF 860
B=ARI(K) JELF 870
A=C*A JELF 880
C=DN*C JELF 890
DN=(GEO(K)+A)/(B+A) JELF 900
9 A=C/B JELF 910
A=1./SQRT(C*C+1.) JELF 920
IF(SN)10,11,11 JELF 930
10 SN=-A JELF 940
GOTO 12 JELF 950
11 SN=A JELF 960
12 CN=C*SN JELF 970
13 IF(SCK)14,2,2 JELF 980
14 A=DN JELF 990
DN=CN JELF1000
CN=A JELF1010
SN=SN/D JELF1020
RETURN JELF1030
END JELF1040