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1985-11-29
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C
C ..................................................................
C
C SUBROUTINE DGT3
C
C PURPOSE
C TO COMPUTE A VECTOR OF DERIVATIVE VALUES GIVEN VECTORS OF
C ARGUMENT VALUES AND CORRESPONDING FUNCTION VALUES.
C
C USAGE
C CALL DGT3(X,Y,Z,NDIM,IER)
C
C DESCRIPTION OF PARAMETERS
C X - GIVEN VECTOR OF ARGUMENT VALUES (DIMENSION NDIM)
C Y - GIVEN VECTOR OF FUNCTION VALUES CORRESPONDING TO X
C (DIMENSION NDIM)
C Z - RESULTING VECTOR OF DERIVATIVE VALUES (DIMENSION
C NDIM)
C NDIM - DIMENSION OF VECTORS X,Y AND Z
C IER - RESULTING ERROR PARAMETER
C IER = -1 - NDIM IS LESS THAN 3
C IER = 0 - NO ERROR
C IER POSITIVE - X(IER) = X(IER-1) OR X(IER) =
C X(IER-2)
C
C REMARKS
C (1) IF IER = -1,2,3, THEN THERE IS NO COMPUTATION.
C (2) IF IER = 4,...,N, THEN THE DERIVATIVE VALUES Z(1)
C ,..., Z(IER-1) HAVE BEEN COMPUTED.
C (3) Z CAN HAVE THE SAME STORAGE ALLOCATION AS X OR Y. IF
C X OR Y IS DISTINCT FROM Z, THEN IT IS NOT DESTROYED.
C
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
C NONE
C
C METHOD
C EXCEPT AT THE ENDPOINTS X(1) AND X(NDIM), Z(I) IS THE
C DERIVATIVE AT X(I) OF THE LAGRANGIAN INTERPOLATION
C POLYNOMIAL OF DEGREE 2 RELEVANT TO THE 3 SUCCESSIVE POINTS
C (X(I+K),Y(I+K)) K = -1,0,1. (SEE HILDEBRAND, F.B.,
C INTRODUCTION TO NUMERICAL ANALYSIS, MC GRAW-HILL, NEW YORK/
C TORONTO/LONDON, 1956, PP. 64-68.)
C
C ..................................................................
C
SUBROUTINE DGT3(X,Y,Z,NDIM,IER)
C
C
DIMENSION X(1),Y(1),Z(1)
C
C TEST OF DIMENSION AND ERROR EXIT IN CASE NDIM IS LESS THAN 3
IER=-1
IF(NDIM-3)8,1,1
C
C PREPARE DIFFERENTIATION LOOP
1 A=X(1)
B=Y(1)
I=2
DY2=X(2)-A
IF(DY2)2,9,2
2 DY2=(Y(2)-B)/DY2
C
C START DIFFERENTIATION LOOP
DO 6 I=3,NDIM
A=X(I)-A
IF(A)3,9,3
3 A=(Y(I)-B)/A
B=X(I)-X(I-1)
IF(B)4,9,4
4 DY1=DY2
DY2=(Y(I)-Y(I-1))/B
DY3=A
A=X(I-1)
B=Y(I-1)
IF(I-3)5,5,6
5 Z(1)=DY1+DY3-DY2
6 Z(I-1)=DY1+DY2-DY3
C END DIFFERENTIATION LOOP
C
C NORMAL EXIT
IER=0
I=NDIM
7 Z(I)=DY2+DY3-DY1
8 RETURN
C
C ERROR EXIT IN CASE OF IDENTICAL ARGUMENTS
9 IER=I
I=I-1
IF(I-2)8,8,7
END