C DDT3 10
C ..................................................................DDT3 20
C DDT3 30
C SUBROUTINE DDET3 DDT3 40
C DDT3 50
C PURPOSE DDT3 60
C TO COMPUTE A VECTOR OF DERIVATIVE VALUES GIVEN A VECTOR OF DDT3 70
C FUNCTION VALUES WHOSE ENTRIES CORRESPOND TO EQUIDISTANTLY DDT3 80
C SPACED ARGUMENT VALUES. DDT3 90
C DDT3 100
C USAGE DDT3 110
C CALL DDET3(H,Y,Z,NDIM,IER) DDT3 120
C DDT3 130
C DESCRIPTION OF PARAMETERS DDT3 140
C H - DOUBLE PRECISION CONSTANT DIFFERENCE BETWEEN DDT3 150
C SUCCESSIVE ARGUMENT VALUES (H IS POSITIVE IF THE DDT3 160
C ARGUMENT VALUES INCREASE AND NEGATIVE OTHERWISE) DDT3 170
C Y - GIVEN VECTOR OF DOUBLE PRECISION FUNCTION VALUES DDT3 180
C (DIMENSION NDIM) DDT3 190
C Z - RESULTING VECTOR OF DOUBLE PRECISION DERIVATIVE DDT3 200
C VALUES (DIMENSION NDIM) DDT3 210
C NDIM - DIMENSION OF VECTORS Y AND Z DDT3 220
C IER - RESULTING ERROR PARAMETER DDT3 230
C IER = -1 - NDIM IS LESS THAN 3 DDT3 240
C IER = 0 - NO ERROR DDT3 250
C IER = 1 - H = 0 DDT3 260
C DDT3 270
C REMARKS DDT3 280
C (1) IF IER = -1,1, THEN THERE IS NO COMPUTATION. DDT3 290
C (2) Z CAN HAVE THE SAME STORAGE ALLOCATION AS Y. IF Y IS DDT3 300
C DISTINCT FROM Z, THEN IT IS NOT DESTROYED. DDT3 310
C DDT3 320
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED DDT3 330
C NONE DDT3 340
C DDT3 350
C METHOD DDT3 360
C IF X IS THE (SUPPRESSED) VECTOR OF ARGUMENT VALUES, THEN DDT3 370
C EXCEPT AT THE ENDPOINTS X(1) AND X(NDIM), Z(I) IS THE DDT3 380
C DERIVATIVE AT X(I) OF THE LAGRANGIAN INTERPOLATION DDT3 390
C POLYNOMIAL OF DEGREE 2 RELEVANT TO THE 3 SUCCESSIVE POINTS DDT3 400
C (X(I+K),Y(I+K)) K = -1,0,1. (SEE HILDEBRAND, F.B., DDT3 410
C INTRODUCTION TO NUMERICAL ANALYSIS, MC-GRAW-HILL, NEW YORK/ DDT3 420
C TORONTO/LONDON, 1956, PP.82-84.) DDT3 430
C DDT3 440
C ..................................................................DDT3 450
C DDT3 460
SUBROUTINE DDET3(H,Y,Z,NDIM,IER) DDT3 470
C DDT3 480
C DDT3 490
DIMENSION Y(1),Z(1) DDT3 500
DOUBLE PRECISION H,Y,Z,HH,YY,A,B DDT3 510
C DDT3 520
C TEST OF DIMENSION DDT3 530
IF(NDIM-3)4,1,1 DDT3 540
C DDT3 550
C TEST OF STEPSIZE DDT3 560
1 IF(H)2,5,2 DDT3 570
C DDT3 580
C PREPARE DIFFERENTIATION LOOP DDT3 590
2 HH=.5D0/H DDT3 600
YY=Y(NDIM-2) DDT3 610
B=Y(2)+Y(2) DDT3 620
B=HH*(B+B-Y(3)-Y(1)-Y(1)-Y(1)) DDT3 630
C DDT3 640
C START DIFFERENTIATION LOOP DDT3 650
DO 3 I=3,NDIM DDT3 660
A=B DDT3 670
B=HH*(Y(I)-Y(I-2)) DDT3 680
3 Z(I-2)=A DDT3 690
C END OF DIFFERENTIATION LOOP DDT3 700
C DDT3 710
C NORMAL EXIT DDT3 720
IER=0 DDT3 730
A=Y(NDIM-1)+Y(NDIM-1) DDT3 740
Z(NDIM)=HH*(Y(NDIM)+Y(NDIM)+Y(NDIM)-A-A+YY) DDT3 750
Z(NDIM-1)=B DDT3 760
RETURN DDT3 770
C DDT3 780
C ERROR EXIT IN CASE NDIM IS LESS THAN 3 DDT3 790
4 IER=-1 DDT3 800
RETURN DDT3 810
C DDT3 820
C ERROR EXIT IN CASE OF ZERO STEPSIZE DDT3 830
5 IER=1 DDT3 840
RETURN DDT3 850
END DDT3 860