C DDT5 10
C ..................................................................DDT5 20
C DDT5 30
C SUBROUTINE DDET5 DDT5 40
C DDT5 50
C PURPOSE DDT5 60
C TO COMPUTE A VECTOR OF DERIVATIVE VALUES GIVEN A VECTOR OF DDT5 70
C FUNCTION VALUES WHOSE ENTRIES CORRESPOND TO EQUIDISTANTLY DDT5 80
C SPACED ARGUMENT VALUES. DDT5 90
C DDT5 100
C USAGE DDT5 110
C CALL DDET5(H,Y,Z,NDIM,IER) DDT5 120
C DDT5 130
C DESCRIPTION OF PARAMETERS DDT5 140
C H - DOUBLE PRECISION CONSTANT DIFFERENCE BETWEEN DDT5 150
C SUCCESSIVE ARGUMENT VALUES (H IS POSITIVE IF THE DDT5 160
C ARGUMENT VALUES INCREASE AND NEGATIVE OTHERWISE) DDT5 170
C Y - GIVEN VECTOR OF DOUBLE PRECISION FUNCTION VALUES DDT5 180
C (DIMENSION NDIM) DDT5 190
C Z - RESULTING VECTOR OF DOUBLE PRECISION DERIVATIVE DDT5 200
C VALUES (DIMENSION NDIM) DDT5 210
C NDIM - DIMENSION OF VECTORS Y AND Z DDT5 220
C IER - RESULTING ERROR PARAMETER DDT5 230
C IER = -1 - NDIM IS LESS THAN 5 DDT5 240
C IER = 0 - NO ERROR DDT5 250
C IER = 1 - H = 0 DDT5 260
C DDT5 270
C REMARKS DDT5 280
C (1) IF IER = -1,1, THEN THERE IS NO COMPUTATION. DDT5 290
C (2) Z CAN HAVE THE SAME STORAGE ALLOCATION AS Y. IF Y IS DDT5 300
C DISTINCT FROM Z, THEN IT IS NOT DESTROYED. DDT5 310
C DDT5 320
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED DDT5 330
C NONE DDT5 340
C DDT5 350
C METHOD DDT5 360
C IF X IS THE (SUPPRESSED) VECTOR OF ARGUMENT VALUES, THEN DDT5 370
C EXCEPT AT THE POINTS X(1),X(2),X(NDIM-1) AND X(NDIM), Z(I) DDT5 380
C IS THE DERIVATIVE AT X(I) OF THE LAGRANGIAN INTERPOLATION DDT5 390
C POLYNOMIAL OF DEGREE 4 RELEVANT TO THE 5 SUCCESSIVE POINTS DDT5 400
C (X(I+K),Y(I+K)) K = -2,-1,...,2. (SEE HILDEBRAND, F.B., DDT5 410
C INTRODUCTION TO NUMERICAL ANALYSIS, MC GRAW-HILL, NEW YORK/ DDT5 420
C TORONTO/LONDON, 1956, PP. 82-84.) DDT5 430
C DDT5 440
C ..................................................................DDT5 450
C DDT5 460
SUBROUTINE DDET5(H,Y,Z,NDIM,IER) DDT5 470
C DDT5 480
C DDT5 490
DIMENSION Y(1),Z(1) DDT5 500
DOUBLE PRECISION H,Y,Z,HH,YY,A,B,C DDT5 510
C DDT5 520
C TEST OF DIMENSION DDT5 530
IF(NDIM-5)4,1,1 DDT5 540
C DDT5 550
C TEST OF STEPSIZE DDT5 560
1 IF(H)2,5,2 DDT5 570
C DDT5 580
C PREPARE DIFFERENTIATION LOOP DDT5 590
2 HH=.08333333333333333D0/H DDT5 600
YY=Y(NDIM-4) DDT5 610
B=HH*(-25.D0*Y(1)+48.D0*Y(2)-36.D0*Y(3)+16.D0*Y(4)-3.D0*Y(5)) DDT5 620
C=HH*(-3.D0*Y(1)-10.D0*Y(2)+18.D0*Y(3)-6.D0*Y(4)+Y(5)) DDT5 630
C DDT5 640
C START DIFFERENTIATION LOOP DDT5 650
DO 3 I=5,NDIM DDT5 660
A=B DDT5 670
B=C DDT5 680
C=HH*(Y(I-4)-Y(I)+8.D0*(Y(I-1)-Y(I-3))) DDT5 690
3 Z(I-4)=A DDT5 700
C END OF DIFFERENTIATION LOOP DDT5 710
C DDT5 720
C NORMAL EXIT DDT5 730
IER=0 DDT5 740
0A=HH*(-YY+6.D0*Y(NDIM-3)-18.D0*Y(NDIM-2)+10.D0*Y(NDIM-1) DDT5 750
1 +3.D0*Y(NDIM)) DDT5 760
0Z(NDIM)=HH*(3.D0*YY-16.D0*Y(NDIM-3)+36.D0*Y(NDIM-2) DDT5 770
1 -48.D0*Y(NDIM-1)+25.D0*Y(NDIM)) DDT5 780
Z(NDIM-1)=A DDT5 790
Z(NDIM-2)=C DDT5 800
Z(NDIM-3)=B DDT5 810
RETURN DDT5 820
C DDT5 830
C ERROR EXIT IN CASE NDIM IS LESS THAN 5 DDT5 840
4 IER=-1 DDT5 850
RETURN DDT5 860
C DDT5 870
C ERROR EXIT IN CASE OF ZERO STEPSIZE DDT5 880
5 IER=1 DDT5 890
RETURN DDT5 900
END DDT5 910