C ALI 10
C ..................................................................ALI 20
C ALI 30
C SUBROUTINE ALI ALI 40
C ALI 50
C PURPOSE ALI 60
C TO INTERPOLATE FUNCTION VALUE Y FOR A GIVEN ARGUMENT VALUE ALI 70
C X USING A GIVEN TABLE (ARG,VAL) OF ARGUMENT AND FUNCTION ALI 80
C VALUES. ALI 90
C ALI 100
C USAGE ALI 110
C CALL ALI (X,ARG,VAL,Y,NDIM,EPS,IER) ALI 120
C ALI 130
C DESCRIPTION OF PARAMETERS ALI 140
C X - THE ARGUMENT VALUE SPECIFIED BY INPUT. ALI 150
C ARG - THE INPUT VECTOR (DIMENSION NDIM) OF ARGUMENT ALI 160
C VALUES OF THE TABLE (NOT DESTROYED). ALI 170
C VAL - THE INPUT VECTOR (DIMENSION NDIM) OF FUNCTION ALI 180
C VALUES OF THE TABLE (DESTROYED). ALI 190
C Y - THE RESULTING INTERPOLATED FUNCTION VALUE. ALI 200
C NDIM - AN INPUT VALUE WHICH SPECIFIES THE NUMBER OF ALI 210
C POINTS IN TABLE (ARG,VAL). ALI 220
C EPS - AN INPUT CONSTANT WHICH IS USED AS UPPER BOUND ALI 230
C FOR THE ABSOLUTE ERROR. ALI 240
C IER - A RESULTING ERROR PARAMETER. ALI 250
C ALI 260
C REMARKS ALI 270
C (1) TABLE (ARG,VAL) SHOULD REPRESENT A SINGLE-VALUED ALI 280
C FUNCTION AND SHOULD BE STORED IN SUCH A WAY, THAT THE ALI 290
C DISTANCES ABS(ARG(I)-X) INCREASE WITH INCREASING ALI 300
C SUBSCRIPT I. TO GENERATE THIS ORDER IN TABLE (ARG,VAL), ALI 310
C SUBROUTINES ATSG, ATSM OR ATSE COULD BE USED IN A ALI 320
C PREVIOUS STAGE. ALI 330
C (2) NO ACTION BESIDES ERROR MESSAGE IN CASE NDIM LESS ALI 340
C THAN 1. ALI 350
C (3) INTERPOLATION IS TERMINATED EITHER IF THE DIFFERENCE ALI 360
C BETWEEN TWO SUCCESSIVE INTERPOLATED VALUES IS ALI 370
C ABSOLUTELY LESS THAN TOLERANCE EPS, OR IF THE ABSOLUTE ALI 380
C VALUE OF THIS DIFFERENCE STOPS DIMINISHING, OR AFTER ALI 390
C (NDIM-1) STEPS. FURTHER IT IS TERMINATED IF THE ALI 400
C PROCEDURE DISCOVERS TWO ARGUMENT VALUES IN VECTOR ARG ALI 410
C WHICH ARE IDENTICAL. DEPENDENT ON THESE FOUR CASES, ALI 420
C ERROR PARAMETER IER IS CODED IN THE FOLLOWING FORM ALI 430
C IER=0 - IT WAS POSSIBLE TO REACH THE REQUIRED ALI 440
C ACCURACY (NO ERROR). ALI 450
C IER=1 - IT WAS IMPOSSIBLE TO REACH THE REQUIRED ALI 460
C ACCURACY BECAUSE OF ROUNDING ERRORS. ALI 470
C IER=2 - IT WAS IMPOSSIBLE TO CHECK ACCURACY BECAUSE ALI 480
C NDIM IS LESS THAN 3, OR THE REQUIRED ACCURACY ALI 490
C COULD NOT BE REACHED BY MEANS OF THE GIVEN ALI 500
C TABLE. NDIM SHOULD BE INCREASED. ALI 510
C IER=3 - THE PROCEDURE DISCOVERED TWO ARGUMENT VALUES ALI 520
C IN VECTOR ARG WHICH ARE IDENTICAL. ALI 530
C ALI 540
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED ALI 550
C NONE ALI 560
C ALI 570
C METHOD ALI 580
C INTERPOLATION IS DONE BY MEANS OF AITKENS SCHEME OF ALI 590
C LAGRANGE INTERPOLATION. ON RETURN Y CONTAINS AN INTERPOLATEDALI 600
C FUNCTION VALUE AT POINT X, WHICH IS IN THE SENSE OF REMARK ALI 610
C (3) OPTIMAL WITH RESPECT TO GIVEN TABLE. FOR REFERENCE, SEE ALI 620
C F.B.HILDEBRAND, INTRODUCTION TO NUMERICAL ANALYSIS, ALI 630
C MCGRAW-HILL, NEW YORK/TORONTO/LONDON, 1956, PP.49-50. ALI 640
C ALI 650
C ..................................................................ALI 660
C ALI 670
SUBROUTINE ALI(X,ARG,VAL,Y,NDIM,EPS,IER) ALI 680
C ALI 690
C ALI 700
DIMENSION ARG(1),VAL(1) ALI 710
IER=2 ALI 720
DELT2=0. ALI 730
IF(NDIM-1)9,7,1 ALI 740
C ALI 750
C START OF AITKEN-LOOP ALI 760
1 DO 6 J=2,NDIM ALI 770
DELT1=DELT2 ALI 780
IEND=J-1 ALI 790
DO 2 I=1,IEND ALI 800
H=ARG(I)-ARG(J) ALI 810
IF(H)2,13,2 ALI 820
2 VAL(J)=(VAL(I)*(X-ARG(J))-VAL(J)*(X-ARG(I)))/H ALI 830
DELT2=ABS(VAL(J)-VAL(IEND)) ALI 840
IF(J-2)6,6,3 ALI 850
3 IF(DELT2-EPS)10,10,4 ALI 860
4 IF(J-5)6,5,5 ALI 870
5 IF(DELT2-DELT1)6,11,11 ALI 880
6 CONTINUE ALI 890
C END OF AITKEN-LOOP ALI 900
C ALI 910
7 J=NDIM ALI 920
8 Y=VAL(J) ALI 930
9 RETURN ALI 940
C ALI 950
C THERE IS SUFFICIENT ACCURACY WITHIN NDIM-1 ITERATION STEPS ALI 960
10 IER=0 ALI 970
GOTO 8 ALI 980
C ALI 990
C TEST VALUE DELT2 STARTS OSCILLATING ALI 1000
11 IER=1 ALI 1010
12 J=IEND ALI 1020
GOTO 8 ALI 1030
C ALI 1040
C THERE ARE TWO IDENTICAL ARGUMENT VALUES IN VECTOR ARG ALI 1050
13 IER=3 ALI 1060
GOTO 12 ALI 1070
END ALI 1080