C DET5 10
C ..................................................................DET5 20
C DET5 30
C SUBROUTINE DET5 DET5 40
C DET5 50
C PURPOSE DET5 60
C TO COMPUTE A VECTOR OF DERIVATIVE VALUES GIVEN A VECTOR OF DET5 70
C FUNCTION VALUES WHOSE ENTRIES CORRESPOND TO EQUIDISTANTLY DET5 80
C SPACED ARGUMENT VALUES. DET5 90
C DET5 100
C USAGE DET5 110
C CALL DET5(H,Y,Z,NDIM,IER) DET5 120
C DET5 130
C DESCRIPTION OF PARAMETERS DET5 140
C H - CONSTANT DIFFERENCE BETWEEN SUCCESSIVE ARGUMENT DET5 150
C VALUES (H IS POSITIVE IF THE ARGUMENT VALUES DET5 160
C INCREASE AND NEGATIVE OTHERWISE) DET5 170
C Y - GIVEN VECTOR OF FUNCTION VALUES (DIMENSION NDIM) DET5 180
C Z - RESULTING VECTOR OF DERIVATIVE VALUES (DIMENSION DET5 190
C NDIM) DET5 200
C NDIM - DIMENSION OF VECTORS Y AND Z DET5 210
C IER - RESULTING ERROR PARAMETER DET5 220
C IER = -1 - NDIM IS LESS THAN 5 DET5 230
C IER = 0 - NO ERROR DET5 240
C IER = 1 - H = 0 DET5 250
C DET5 260
C REMARKS DET5 270
C (1) IF IER = -1,1, THEN THERE IS NO COMPUTATION. DET5 280
C (2) Z CAN HAVE THE SAME STORAGE ALLOCATION AS Y. IF Y IS DET5 290
C DISTINCT FROM Z, THEN IT IS NOT DESTROYED. DET5 300
C DET5 310
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED DET5 320
C NONE DET5 330
C DET5 340
C METHOD DET5 350
C IF X IS THE (SUPPRESSED) VECTOR OF ARGUMENT VALUES, THEN DET5 360
C EXCEPT AT THE POINTS X(1),X(2),X(NDIM-1) AND X(NDIM), Z(I) DET5 370
C IS THE DERIVATIVE AT X(I) OF THE LAGRANGIAN INTERPOLATION DET5 380
C POLYNOMIAL OF DEGREE 4 RELEVANT TO THE 5 SUCCESSIVE POINTS DET5 390
C (X(I+K),Y(I+K)) K = -2,-1,...,2. (SEE HILDEBRAND, F.B., DET5 400
C INTRODUCTION TO NUMERICAL ANALYSIS, MC GRAW-HILL, NEW YORK/ DET5 410
C TORONTO/LONDON, 1956, PP. 82-84.) DET5 420
C DET5 430
C ..................................................................DET5 440
C DET5 450
SUBROUTINE DET5(H,Y,Z,NDIM,IER) DET5 460
C DET5 470
C DET5 480
DIMENSION Y(1),Z(1) DET5 490
C DET5 500
C TEST OF DIMENSION DET5 510
IF(NDIM-5)4,1,1 DET5 520
C DET5 530
C TEST OF STEPSIZE DET5 540
1 IF(H)2,5,2 DET5 550
C DET5 560
C PREPARE DIFFERENTIATION LOOP DET5 570
2 HH=.08333333/H DET5 580
YY=Y(NDIM-4) DET5 590
B=HH*(-25.*Y(1)+48.*Y(2)-36.*Y(3)+16.*Y(4)-3.*Y(5)) DET5 600
C=HH*(-3.*Y(1)-10.*Y(2)+18.*Y(3)-6.*Y(4)+Y(5)) DET5 610
C DET5 620
C START DIFFERENTIATION LOOP DET5 630
DO 3 I=5,NDIM DET5 640
A=B DET5 650
B=C DET5 660
C=HH*(Y(I-4)-Y(I)+8.*(Y(I-1)-Y(I-3))) DET5 670
3 Z(I-4)=A DET5 680
C END OF DIFFERENTIATION LOOP DET5 690
C DET5 700
C NORMAL EXIT DET5 710
IER=0 DET5 720
A=HH*(-YY+6.*Y(NDIM-3)-18.*Y(NDIM-2)+10.*Y(NDIM-1)+3.*Y(NDIM)) DET5 730
0Z(NDIM)=HH*(3.*YY-16.*Y(NDIM-3)+36.*Y(NDIM-2)-48.*Y(NDIM-1) DET5 740
1 +25.*Y(NDIM)) DET5 750
Z(NDIM-1)=A DET5 760
Z(NDIM-2)=C DET5 770
Z(NDIM-3)=B DET5 780
RETURN DET5 790
C DET5 800
C ERROR EXIT IN CASE NDIM IS LESS THAN 5 DET5 810
4 IER=-1 DET5 820
RETURN DET5 830
C DET5 840
C ERROR EXIT IN CASE OF ZERO STEPSIZE DET5 850
5 IER=1 DET5 860
RETURN DET5 870
END DET5 880