C DTEU 10
C ..................................................................DTEU 20
C DTEU 30
C SUBROUTINE DTEUL DTEU 40
C DTEU 50
C PURPOSE DTEU 60
C COMPUTE THE SUM OF FCT(K) FOR K FROM ONE UP TO INFINITY. DTEU 70
C DTEU 80
C USAGE DTEU 90
C CALL DTEUL(FCT,SUM,MAX,EPS,IER) DTEU 100
C PARAMETER FCT REQUIRES AN EXTERNAL STATEMENT. DTEU 110
C DTEU 120
C DESCRIPTION OF PARAMETERS DTEU 130
C FCT - NAME OF AN EXTERNAL DOUBLE PRECISION FUNCTION DTEU 140
C SUBPROGRAM USED. IT COMPUTES THE K-TH TERM OF THE DTEU 150
C SERIES TO ANY GIVEN INDEX K. DTEU 160
C SUM - RESULTANT VALUE IN DOUBLE PRECISION CONTAINING ON DTEU 170
C RETURN THE SUM OF THE GIVEN SERIES. DTEU 180
C MAX - INPUT VALUE, WHICH SPECIFIES THE MAXIMAL NUMBER DTEU 190
C OF TERMS OF THE SERIES THAT ARE RESPECTED. DTEU 200
C EPS - SINGLE PRECISION INPUT VALUE, WHICH SPECIFIES THE DTEU 210
C UPPER BOUND OF THE RELATIVE ERROR. DTEU 220
C SUMMATION IS STOPPED AS SOON AS FIVE TIMES IN DTEU 230
C SUCCESSION THE ABSOLUTE VALUE OF THE TERMS OF THE DTEU 240
C TRANSFORMED SERIES ARE FOUND TO BE LESS THAN DTEU 250
C EPS*(ABSOLUTE VALUE OF CURRENT SUM). DTEU 260
C IER - RESULTANT ERROR PARAMETER CODED IN THE FOLLOWING DTEU 270
C FORM DTEU 280
C IER=0 - NO ERROR DTEU 290
C IER=1 - REQUIRED ACCURACY NOT REACHED WITH DTEU 300
C MAXIMAL NUMBER OF TERMS DTEU 310
C IER=-1 - THE INTEGER MAX IS LESS THAN ONE. DTEU 320
C DTEU 330
C REMARKS DTEU 340
C NO ACTION BESIDES ERROR MESSAGE IN CASE MAX LESS THAN ONE. DTEU 350
C DTEU 360
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED DTEU 370
C THE EXTERNAL FUNCTION SUBPROGRAM FCT(K) MUST BE FURNISHED DTEU 380
C BY THE USER. DTEU 390
C DTEU 400
C METHOD DTEU 410
C EVALUATION IS DONE BY MEANS OF A SUITABLY REFINED EULER DTEU 420
C TRANSFORMATION. FOR REFERENCE, SEE DTEU 430
C F.B.HILDEBRAND, INTRODUCTION TO NUMERICAL ANALYSIS, DTEU 440
C MCGRAW/HILL, NEW YORK/TORONTO/LONDON, 1956, PP.155-160, AND DTEU 450
C P. NAUR, REPORT ON THE ALGORITHMIC LANGUAGE ALGOL 60, DTEU 460
C CACM, VOL.3, ISS.5 (1960), PP.311. DTEU 470
C DTEU 480
C ..................................................................DTEU 490
C DTEU 500
SUBROUTINE DTEUL (FCT,SUM,MAX,EPS,IER) DTEU 510
C DTEU 520
DIMENSION Y(15) DTEU 530
DOUBLE PRECISION FCT,SUM,Y,AMN,AMP DTEU 540
C DTEU 550
C TEST ON WRONG INPUT PARAMETER MAX DTEU 560
C DTEU 570
IF(MAX)1,1,2 DTEU 580
1 IER=-1 DTEU 590
GOTO 12 DTEU 600
C DTEU 610
C INITIALIZE EULER TRANSFORMATION DTEU 620
C DTEU 630
2 IER=1 DTEU 640
I=1 DTEU 650
M=1 DTEU 660
N=1 DTEU 670
Y(1)=FCT(N) DTEU 680
SUM=Y(1)*.5D0 DTEU 690
C DTEU 700
C START EULER-LOOP DTEU 710
C DTEU 720
3 J=0 DTEU 730
4 I=I+1 DTEU 740
IF(I-MAX)5,5,12 DTEU 750
5 N=I DTEU 760
AMN=FCT(N) DTEU 770
DO 6 K=1,M DTEU 780
AMP=(AMN+Y(K))*.5D0 DTEU 790
Y(K)=AMN DTEU 800
6 AMN=AMP DTEU 810
C DTEU 820
C CHECK EULER TRANSFORMATION DTEU 830
C DTEU 840
IF(DABS(AMN)-DABS(Y(M)))7,9,9 DTEU 850
7 IF(M-15)8,9,9 DTEU 860
8 M=M+1 DTEU 870
Y(M)=AMN DTEU 880
AMN=.5D0*AMN DTEU 890
C DTEU 900
C UPDATE SUM DTEU 910
C DTEU 920
9 SUM=SUM+AMN DTEU 930
IF(ABS(SNGL(AMN))-EPS*ABS(SNGL(SUM)))10,10,3 DTEU 940
C DTEU 950
C TEST END OF PROCEDURE DTEU 960
C DTEU 970
10 J=J+1 DTEU 980
IF(J-5)4,11,11 DTEU 990
11 IER=0 DTEU1000
12 RETURN DTEU1010
END DTEU1020