C DDGT 10
C ..................................................................DDGT 20
C DDGT 30
C SUBROUTINE DDGT3 DDGT 40
C DDGT 50
C PURPOSE DDGT 60
C TO COMPUTE A VECTOR OF DERIVATIVE VALUES GIVEN VECTORS OF DDGT 70
C ARGUMENT VALUES AND CORRESPONDING FUNCTION VALUES. DDGT 80
C DDGT 90
C USAGE DDGT 100
C CALL DDGT3(X,Y,Z,NDIM,IER) DDGT 110
C DDGT 120
C DESCRIPTION OF PARAMETERS DDGT 130
C X - GIVEN VECTOR OF DOUBLE PRECISION ARGUMENT VALUES DDGT 140
C (DIMENSION NDIM) DDGT 150
C Y - GIVEN VECTOR OF DOUBLE PRECISION FUNCTION VALUES DDGT 160
C CORRESPONDING TO X (DIMENSION NDIM) DDGT 170
C Z - RESULTING VECTOR OF DOUBLE PRECISION DERIVATIVE DDGT 180
C VALUES (DIMENSION NDIM) DDGT 190
C NDIM - DIMENSION OF VECTORS X,Y AND Z DDGT 200
C IER - RESULTING ERROR PARAMETER DDGT 210
C IER = -1 - NDIM IS LESS THAN 3 DDGT 220
C IER = 0 - NO ERROR DDGT 230
C IER POSITIVE - X(IER) = X(IER-1) OR X(IER) = DDGT 240
C X(IER-2) DDGT 250
C DDGT 260
C REMARKS DDGT 270
C (1) IF IER = -1,2,3, THEN THERE IS NO COMPUTATION. DDGT 280
C (2) IF IER = 4,...,N, THEN THE DERIVATIVE VALUES Z(1) DDGT 290
C ,..., Z(IER-1) HAVE BEEN COMPUTED. DDGT 300
C (3) Z CAN HAVE THE SAME STORAGE ALLOCATION AS X OR Y. IF DDGT 310
C X OR Y IS DISTINCT FROM Z, THEN IT IS NOT DESTROYED. DDGT 320
C DDGT 330
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED DDGT 340
C NONE DDGT 350
C DDGT 360
C METHOD DDGT 370
C EXCEPT AT THE ENDPOINTS X(1) AND X(NDIM), Z(I) IS THE DDGT 380
C DERIVATIVE AT X(I) OF THE LAGRANGIAN INTERPOLATION DDGT 390
C POLYNOMIAL OF DEGREE 2 RELEVANT TO THE 3 SUCCESSIVE POINTS DDGT 400
C (X(I+K),Y(I+K)) K = -1,0,1. (SEE HILDEBRAND, F.B., DDGT 410
C INTRODUCTION TO NUMERICAL ANALYSIS, MC GRAW-HILL, NEW YORK/ DDGT 420
C TORONTO/LONDON, 1956, PP. 64-68.) DDGT 430
C DDGT 440
C ..................................................................DDGT 450
C DDGT 460
SUBROUTINE DDGT3(X,Y,Z,NDIM,IER) DDGT 470
C DDGT 480
C DDGT 490
DIMENSION X(1),Y(1),Z(1) DDGT 500
DOUBLE PRECISION X,Y,Z,DY1,DY2,DY3,A,B DDGT 510
C DDGT 520
C TEST OF DIMENSION AND ERROR EXIT IN CASE NDIM IS LESS THAN 3 DDGT 530
IER=-1 DDGT 540
IF(NDIM-3)8,1,1 DDGT 550
C DDGT 560
C PREPARE DIFFERENTIATION LOOP DDGT 570
1 A=X(1) DDGT 580
B=Y(1) DDGT 590
I=2 DDGT 600
DY2=X(2)-A DDGT 610
IF(DY2)2,9,2 DDGT 620
2 DY2=(Y(2)-B)/DY2 DDGT 630
C DDGT 640
C START DIFFERENTIATION LOOP DDGT 650
DO 6 I=3,NDIM DDGT 660
A=X(I)-A DDGT 670
IF(A)3,9,3 DDGT 680
3 A=(Y(I)-B)/A DDGT 690
B=X(I)-X(I-1) DDGT 700
IF(B)4,9,4 DDGT 710
4 DY1=DY2 DDGT 720
DY2=(Y(I)-Y(I-1))/B DDGT 730
DY3=A DDGT 740
A=X(I-1) DDGT 750
B=Y(I-1) DDGT 760
IF(I-3)5,5,6 DDGT 770
5 Z(1)=DY1+DY3-DY2 DDGT 780
6 Z(I-1)=DY1+DY2-DY3 DDGT 790
C END OF DIFFERENTIATION LOOP DDGT 800
C DDGT 810
C NORMAL EXIT DDGT 820
IER=0 DDGT 830
I=NDIM DDGT 840
7 Z(I)=DY2+DY3-DY1 DDGT 850
8 RETURN DDGT 860
C DDGT 870
C ERROR EXIT IN CASE OF IDENTICAL ARGUMENTS DDGT 880
9 IER=I DDGT 890
I=I-1 DDGT 900
IF(I-2)8,8,7 DDGT 910
END DDGT 920