C DRTW 10
C ..................................................................DRTW 20
C DRTW 30
C SUBROUTINE DRTWI DRTW 40
C DRTW 50
C PURPOSE DRTW 60
C TO SOLVE GENERAL NONLINEAR EQUATIONS OF THE FORM X=FCT(X) DRTW 70
C BY MEANS OF WEGSTEIN-S ITERATION METHOD. DRTW 80
C DRTW 90
C USAGE DRTW 100
C CALL DRTWI (X,VAL,FCT,XST,EPS,IEND,IER) DRTW 110
C PARAMETER FCT REQUIRES AN EXTERNAL STATEMENT. DRTW 120
C DRTW 130
C DESCRIPTION OF PARAMETERS DRTW 140
C X - DOUBLE PRECISION RESULTANT ROOT OF EQUATION DRTW 150
C X=FCT(X). DRTW 160
C VAL - DOUBLE PRECISION RESULTANT VALUE OF X-FCT(X) DRTW 170
C AT ROOT X. DRTW 180
C FCT - NAME OF THE EXTERNAL DOUBLE PRECISION FUNCTION DRTW 190
C SUBPROGRAM USED. DRTW 200
C XST - DOUBLE PRECISION INPUT VALUE WHICH SPECIFIES THE DRTW 210
C INITIAL GUESS OF THE ROOT X. DRTW 220
C EPS - SINGLE PRECISION INPUT VALUE WHICH SPECIFIES THE DRTW 230
C UPPER BOUND OF THE ERROR OF RESULT X. DRTW 240
C IEND - MAXIMUM NUMBER OF ITERATION STEPS SPECIFIED. DRTW 250
C IER - RESULTANT ERROR PARAMETER CODED AS FOLLOWS DRTW 260
C IER=0 - NO ERROR, DRTW 270
C IER=1 - NO CONVERGENCE AFTER IEND ITERATION STEPS,DRTW 280
C IER=2 - AT ANY ITERATION STEP THE DENOMINATOR OF DRTW 290
C ITERATION FORMULA WAS EQUAL TO ZERO. DRTW 300
C DRTW 310
C REMARKS DRTW 320
C THE PROCEDURE IS BYPASSED AND GIVES THE ERROR MESSAGE IER=2 DRTW 330
C IF AT ANY ITERATION STEP THE DENOMINATOR OF ITERATION DRTW 340
C FORMULA WAS EQUAL TO ZERO. THAT MEANS THAT THERE IS AT DRTW 350
C LEAST ONE POINT IN THE RANGE IN WHICH ITERATION MOVES WITH DRTW 360
C DERIVATIVE OF FCT(X) EQUAL TO 1. DRTW 370
C DRTW 380
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED DRTW 390
C THE EXTERNAL DOUBLE PRECISION FUNCTION SUBPROGRAM FCT(X) DRTW 400
C MUST BE FURNISHED BY THE USER. DRTW 410
C DRTW 420
C METHOD DRTW 430
C SOLUTION OF EQUATION X=FCT(X) IS DONE BY MEANS OF DRTW 440
C WEGSTEIN-S ITERATION METHOD, WHICH STARTS AT THE INITIAL DRTW 450
C GUESS XST OF A ROOT X. ONE ITERATION STEP REQUIRES ONE DRTW 460
C EVALUATION OF FCT(X). FOR TEST ON SATISFACTORY ACCURACY SEE DRTW 470
C FORMULAE (2) OF MATHEMATICAL DESCRIPTION. DRTW 480
C FOR REFERENCE, SEE DRTW 490
C (1) G. N. LANCE, NUMERICAL METHODS FOR HIGH SPEED COMPUTERS,DRTW 500
C ILIFFE, LONDON, 1960, PP.134-138, DRTW 510
C (2) J. WEGSTEIN, ALGORITHM 2, CACM, VOL.3, ISS.2 (1960), DRTW 520
C PP.74, DRTW 530
C (3) H.C. THACHER, ALGORITHM 15, CACM, VOL.3, ISS.8 (1960), DRTW 540
C PP.475, DRTW 550
C (4) J.G. HERRIOT, ALGORITHM 26, CACM, VOL.3, ISS.11 (1960), DRTW 560
C PP.603. DRTW 570
C DRTW 580
C ..................................................................DRTW 590
C DRTW 600
SUBROUTINE DRTWI(X,VAL,FCT,XST,EPS,IEND,IER) DRTW 610
C DRTW 620
C DRTW 630
DOUBLE PRECISION X,VAL,FCT,XST,A,B,D,TOL DRTW 640
C DRTW 650
C PREPARE ITERATION DRTW 660
IER=0 DRTW 670
TOL=XST DRTW 680
X=FCT(TOL) DRTW 690
A=X-XST DRTW 700
B=-A DRTW 710
TOL=X DRTW 720
VAL=X-FCT(TOL) DRTW 730
C DRTW 740
C DRTW 750
C START ITERATION LOOP DRTW 760
DO 6 I=1,IEND DRTW 770
IF(VAL)1,7,1 DRTW 780
C DRTW 790
C EQUATION IS NOT SATISFIED BY X DRTW 800
1 B=B/VAL-1.D0 DRTW 810
IF(B)2,8,2 DRTW 820
C DRTW 830
C ITERATION IS POSSIBLE DRTW 840
2 A=A/B DRTW 850
X=X+A DRTW 860
B=VAL DRTW 870
TOL=X DRTW 880
VAL=X-FCT(TOL) DRTW 890
C DRTW 900
C TEST ON SATISFACTORY ACCURACY DRTW 910
TOL=EPS DRTW 920
D=DABS(X) DRTW 930
IF(D-1.D0)4,4,3 DRTW 940
3 TOL=TOL*D DRTW 950
4 IF(DABS(A)-TOL)5,5,6 DRTW 960
5 IF(DABS(VAL)-1.D1*TOL)7,7,6 DRTW 970
6 CONTINUE DRTW 980
C END OF ITERATION LOOP DRTW 990
C DRTW1000
C DRTW1010
C NO CONVERGENCE AFTER IEND ITERATION STEPS. ERROR RETURN. DRTW1020
IER=1 DRTW1030
7 RETURN DRTW1040
C DRTW1050
C ERROR RETURN IN CASE OF ZERO DIVISOR DRTW1060
8 IER=2 DRTW1070
RETURN DRTW1080
END DRTW1090