C CEL1 10
C ..................................................................CEL1 20
C CEL1 30
C SUBROUTINE CEL1 CEL1 40
C CEL1 50
C PURPOSE CEL1 60
C CALCULATE COMPLETE ELLIPTIC INTEGRAL OF FIRST KIND CEL1 70
C CEL1 80
C USAGE CEL1 90
C CALL CEL1(RES,AK,IER) CEL1 100
C CEL1 110
C DESCRIPTION OF PARAMETERS CEL1 120
C RES - RESULT VALUE CEL1 130
C AK - MODULUS (INPUT) CEL1 140
C IER - RESULTANT ERROR CODE WHERE CEL1 150
C IER=0 NO ERROR CEL1 160
C IER=1 AK NOT IN RANGE -1 TO +1 CEL1 170
C CEL1 180
C REMARKS CEL1 190
C THE RESULT IS SET TO 1.7E38 IF ABS(AK) GE 1 CEL1 200
C FOR MODULUS AK AND COMPLEMENTARY MODULUS CK, CEL1 210
C EQUATION AK*AK+CK*CK=1.0 IS USED. CEL1 220
C AK MUST BE IN THE RANGE -1 TO +1 CEL1 230
C CEL1 240
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED CEL1 250
C NONE CEL1 260
C CEL1 270
C METHOD CEL1 280
C DEFINITION CEL1 290
C CEL1(AK)=INTEGRAL(1/SQRT((1+T*T)*(1+(CK*T)**2)), SUMMED CEL1 300
C OVER T FROM 0 TO INFINITY). CEL1 310
C EQUIVALENT ARE THE DEFINITIONS CEL1 320
C CEL1(AK)=INTEGRAL(1/(COS(T)SQRT(1+(CK*TAN(T))**2)),SUMMED CEL1 330
C OVER T FROM 0 TO PI/2), CEL1 340
C CEL1(AK)=INTEGRAL(1/SQRT(1-(AK*SIN(T))**2),SUMMED OVER T CEL1 350
C FROM 0 TO PI/2), WHERE K=SQRT(1.-CK*CK). CEL1 360
C EVALUATION CEL1 370
C LANDENS TRANSFORMATION IS USED FOR CALCULATION. CEL1 380
C REFERENCE CEL1 390
C R.BULIRSCH, 'NUMERICAL CALCULATION OF ELLIPTIC INTEGRALS CEL1 400
C AND ELLIPTIC FUNCTIONS', HANDBOOK SERIES SPECIAL FUNCTIONS, CEL1 410
C NUMERISCHE MATHEMATIK VOL. 7, 1965, PP. 78-90. CEL1 420
C CEL1 430
C ..................................................................CEL1 440
C CEL1 450
SUBROUTINE CEL1(RES,AK,IER) CEL1 460
IER=0 CEL1 470
ARI=2. CEL1 480
GEO=(0.5-AK)+0.5 CEL1 490
GEO=GEO+GEO*AK CEL1 500
RES=0.5 CEL1 510
IF(GEO)1,2,4 CEL1 520
1 IER=1 CEL1 530
2 RES=1.7E38 CEL1 540
RETURN CEL1 550
3 GEO=GEO*AARI CEL1 560
4 GEO=SQRT(GEO) CEL1 570
GEO=GEO+GEO CEL1 580
AARI=ARI CEL1 590
ARI=ARI+GEO CEL1 600
RES=RES+RES CEL1 610
IF(GEO/AARI-0.9999)3,5,5 CEL1 620
5 RES=RES/ARI*6.283185E0 CEL1 630
RETURN CEL1 640
END CEL1 650