C DJEL 10
C ..................................................................DJEL 20
C DJEL 30
C SUBROUTINE DJELF DJEL 40
C DJEL 50
C PURPOSE DJEL 60
C COMPUTES THE THREE JACOBIAN ELLIPTIC FUNCTIONS SN, CN, DN. DJEL 70
C DJEL 80
C USAGE DJEL 90
C CALL DJELF(SN,CN,DN,X,SCK) DJEL 100
C DJEL 110
C DESCRIPTION OF PARAMETERS DJEL 120
C SN - RESULT VALUE SN(X) IN DOUBLE PRECISION DJEL 130
C CN - RESULT VALUE CN(X) IN DOUBLE PRECISION DJEL 140
C DN - RESULT VALUE DN(X) IN DOUBLE PRECISION DJEL 150
C X - DOUBLE PRECISION ARGUMENT OF JACOBIAN ELLIPTIC DJEL 160
C FUNCTIONS DJEL 170
C SCK - SQUARE OF COMPLEMENTARY MODULUS IN DOUBLE PRECISION DJEL 180
C DJEL 190
C REMARKS DJEL 200
C NONE DJEL 210
C DJEL 220
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED DJEL 230
C NONE DJEL 240
C DJEL 250
C METHOD DJEL 260
C DEFINITION DJEL 270
C X=INTEGRAL(1/SQRT((1-T*T)*(1-(K*T)**2)), SUMMED OVER DJEL 280
C T FROM 0 TO SN), WHERE K=SQRT(1-SCK). DJEL 290
C SN*SN + CN*CN = 1 DJEL 300
C (K*SN)**2 + DN**2 = 1. DJEL 310
C EVALUATION DJEL 320
C CALCULATION IS DONE USING THE PROCESS OF THE ARITHMETIC DJEL 330
C GEOMETRIC MEAN TOGETHER WITH GAUSS DESCENDING TRANSFORMATIONDJEL 340
C BEFORE INVERSION OF THE INTEGRAL TAKES PLACE. DJEL 350
C REFERENCE DJEL 360
C R. BULIRSCH, NUMERICAL CALCULATION OF ELLIPTIC INTEGRALS ANDDJEL 370
C ELLIPTIC FUNCTIOMS. DJEL 380
C HANDBOOK SERIES OF SPECIAL FUNCTIONS DJEL 390
C NUMERISCHE MATHEMATIK VOL. 7, 1965, PP. 78-90. DJEL 400
C DJEL 410
C ..................................................................DJEL 420
C DJEL 430
SUBROUTINE DJELF(SN,CN,DN,X,SCK) DJEL 440
C DJEL 450
DIMENSION ARI(12),GEO(12) DJEL 460
DOUBLE PRECISION SN,CN,DN,X,SCK,ARI,GEO,CM,Y,A,B,C,D DJEL 470
C DJEL 480
C TEST MODULUS DJEL 490
C DJEL 500
CM=SCK DJEL 510
Y=X DJEL 520
IF(SCK)3,1,4 DJEL 530
1 D=DEXP(X) DJEL 540
A=1.D0/D DJEL 550
B=A+D DJEL 560
CN=2.D0/B DJEL 570
DN=CN DJEL 580
A=(D-A)/2.D0 DJEL 590
SN=A*CN DJEL 600
C DEGENERATE CASE SCK=0 GIVES RESULTS DJEL 610
C CN X = DN X = 1/COSH X DJEL 620
C SN X = TANH X DJEL 630
2 RETURN DJEL 640
C DJEL 650
C JACOBIS MODULUS TRANSFORMATION DJEL 660
C DJEL 670
3 D=1.D0-SCK DJEL 680
CM=-SCK/D DJEL 690
D=DSQRT(D) DJEL 700
Y=D*X DJEL 710
4 A=1.D0 DJEL 720
DN=1.D0 DJEL 730
DO 6 I=1,12 DJEL 740
L=I DJEL 750
ARI(I)=A DJEL 760
CM=DSQRT(CM) DJEL 770
GEO(I)=CM DJEL 780
C=(A+CM)*.5D0 DJEL 790
IF(DABS(A-CM)-1.D-9*A)7,7,5 DJEL 800
5 CM=A*CM DJEL 810
6 A=C DJEL 820
C DJEL 830
C START BACKWARD RECURSION DJEL 840
C DJEL 850
7 Y=C*Y DJEL 860
SN=DSIN(Y) DJEL 870
CN=DCOS(Y) DJEL 880
IF(SN)8,13,8 DJEL 890
8 A=CN/SN DJEL 900
C=A*C DJEL 910
DO 9 I=1,L DJEL 920
K=L-I+1 DJEL 930
B=ARI(K) DJEL 940
A=C*A DJEL 950
C=DN*C DJEL 960
DN=(GEO(K)+A)/(B+A) DJEL 970
9 A=C/B DJEL 980
A=1.D0/DSQRT(C*C+1.D0) DJEL 990
IF(SN)10,11,11 DJEL1000
10 SN=-A DJEL1010
GOTO 12 DJEL1020
11 SN=A DJEL1030
12 CN=C*SN DJEL1040
13 IF(SCK)14,2,2 DJEL1050
14 A=DN DJEL1060
DN=CN DJEL1070
CN=A DJEL1080
SN=SN/D DJEL1090
RETURN DJEL1100
END DJEL1110