C DGT3 10
C ..................................................................DGT3 20
C DGT3 30
C SUBROUTINE DGT3 DGT3 40
C DGT3 50
C PURPOSE DGT3 60
C TO COMPUTE A VECTOR OF DERIVATIVE VALUES GIVEN VECTORS OF DGT3 70
C ARGUMENT VALUES AND CORRESPONDING FUNCTION VALUES. DGT3 80
C DGT3 90
C USAGE DGT3 100
C CALL DGT3(X,Y,Z,NDIM,IER) DGT3 110
C DGT3 120
C DESCRIPTION OF PARAMETERS DGT3 130
C X - GIVEN VECTOR OF ARGUMENT VALUES (DIMENSION NDIM) DGT3 140
C Y - GIVEN VECTOR OF FUNCTION VALUES CORRESPONDING TO X DGT3 150
C (DIMENSION NDIM) DGT3 160
C Z - RESULTING VECTOR OF DERIVATIVE VALUES (DIMENSION DGT3 170
C NDIM) DGT3 180
C NDIM - DIMENSION OF VECTORS X,Y AND Z DGT3 190
C IER - RESULTING ERROR PARAMETER DGT3 200
C IER = -1 - NDIM IS LESS THAN 3 DGT3 210
C IER = 0 - NO ERROR DGT3 220
C IER POSITIVE - X(IER) = X(IER-1) OR X(IER) = DGT3 230
C X(IER-2) DGT3 240
C DGT3 250
C REMARKS DGT3 260
C (1) IF IER = -1,2,3, THEN THERE IS NO COMPUTATION. DGT3 270
C (2) IF IER = 4,...,N, THEN THE DERIVATIVE VALUES Z(1) DGT3 280
C ,..., Z(IER-1) HAVE BEEN COMPUTED. DGT3 290
C (3) Z CAN HAVE THE SAME STORAGE ALLOCATION AS X OR Y. IF DGT3 300
C X OR Y IS DISTINCT FROM Z, THEN IT IS NOT DESTROYED. DGT3 310
C DGT3 320
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED DGT3 330
C NONE DGT3 340
C DGT3 350
C METHOD DGT3 360
C EXCEPT AT THE ENDPOINTS X(1) AND X(NDIM), Z(I) IS THE DGT3 370
C DERIVATIVE AT X(I) OF THE LAGRANGIAN INTERPOLATION DGT3 380
C POLYNOMIAL OF DEGREE 2 RELEVANT TO THE 3 SUCCESSIVE POINTS DGT3 390
C (X(I+K),Y(I+K)) K = -1,0,1. (SEE HILDEBRAND, F.B., DGT3 400
C INTRODUCTION TO NUMERICAL ANALYSIS, MC GRAW-HILL, NEW YORK/ DGT3 410
C TORONTO/LONDON, 1956, PP. 64-68.) DGT3 420
C DGT3 430
C ..................................................................DGT3 440
C DGT3 450
SUBROUTINE DGT3(X,Y,Z,NDIM,IER) DGT3 460
C DGT3 470
C DGT3 480
DIMENSION X(1),Y(1),Z(1) DGT3 490
C DGT3 500
C TEST OF DIMENSION AND ERROR EXIT IN CASE NDIM IS LESS THAN 3 DGT3 510
IER=-1 DGT3 520
IF(NDIM-3)8,1,1 DGT3 530
C DGT3 540
C PREPARE DIFFERENTIATION LOOP DGT3 550
1 A=X(1) DGT3 560
B=Y(1) DGT3 570
I=2 DGT3 580
DY2=X(2)-A DGT3 590
IF(DY2)2,9,2 DGT3 600
2 DY2=(Y(2)-B)/DY2 DGT3 610
C DGT3 620
C START DIFFERENTIATION LOOP DGT3 630
DO 6 I=3,NDIM DGT3 640
A=X(I)-A DGT3 650
IF(A)3,9,3 DGT3 660
3 A=(Y(I)-B)/A DGT3 670
B=X(I)-X(I-1) DGT3 680
IF(B)4,9,4 DGT3 690
4 DY1=DY2 DGT3 700
DY2=(Y(I)-Y(I-1))/B DGT3 710
DY3=A DGT3 720
A=X(I-1) DGT3 730
B=Y(I-1) DGT3 740
IF(I-3)5,5,6 DGT3 750
5 Z(1)=DY1+DY3-DY2 DGT3 760
6 Z(I-1)=DY1+DY2-DY3 DGT3 770
C END DIFFERENTIATION LOOP DGT3 780
C DGT3 790
C NORMAL EXIT DGT3 800
IER=0 DGT3 810
I=NDIM DGT3 820
7 Z(I)=DY2+DY3-DY1 DGT3 830
8 RETURN DGT3 840
C DGT3 850
C ERROR EXIT IN CASE OF IDENTICAL ARGUMENTS DGT3 860
9 IER=I DGT3 870
I=I-1 DGT3 880
IF(I-2)8,8,7 DGT3 890
END DGT3 900